The 23-year-old Reading-born midfielder was joined by Dundee United winger Gary Mackay-Steven and Peterborough winger George Boyd in getting his first call-up ahead of the World Cup qualifiers against Wales and Serbia.
Boyd, who is currently on loan at Hull, previously featured for Scotland B in 2009 but had never made a full squad.
Southampton left-back Danny Fox has been recalled to the squad while there is no place for Rangers' Lee Wallace or Phil Bardsley, who has not played for Sunderland since January 19.
Blackpool winger Matt Phillips and QPR forward Jamie Mackie both drop out of the squad as does Celtic captain Scott Brown, whose season appears to be over because of an abductor injury.
In-form Hibernian striker Leigh Griffiths was not included but Chris Burke retains his place after Strachan handed him his first international cap in more than six years in the 1-0 friendly win over Estonia last month.
Bridcutt, who began his career in the Chelsea youth ranks, qualifies through his grandfather from Edinburgh.
The holding midfielder's inclusion is subject to Scottish Football Association paperwork being completed.
Both Strachan and assistant Mark McGhee, a former Brighton manager, have watched him closely.
Strachan said: "Liam is a guy I've been watching. I've seen a lot of his games.
"At the time I didn't realise he could possibly play for Scotland.
"Mark McGhee, who lives in the Brighton area, has seen a lot of Liam and he did his homework into the type of guy Liam was and did he want to play for Scotland.
"We've put that all together and we've come to the conclusion that he's good enough."
Former Scotland Under-21 international Mackay-Steven has returned to top form for United in recent weeks after an injury-hit first half of the season.
Strachan added: "I've seen him a couple of times recently and he makes an impression on the game, that's for sure."
Boyd has scored two goals in three games for Hull since his loan move, which followed an aborted attempt by former Scotland manager Alex McLeish to sign the player during his short reign at Nottingham Forest.
Forest pulled out of a deal to sign the 27-year-old because of the results of an eye test, a decision which played a major role in McLeish's subsequent departure form the City Ground.
Strachan said: "He is an elegant player, a good passer and he scores a fair amount of goals for an attacking midfield player."
The Scotland boss also confirmed Gary Caldwell will be captain in the absence of Darren Fletcher.
Meanwhile, Gordon Strachan has urged his Scotland players to focus on each other's strengths rather than be daunted by the talents of Gareth Bale when Wales visit Hampden.
The World Cup qualifier on March 22 will be Strachan's first competitive match since replacing Craig Levein as national team manager.
Much of the build-up will centre on the impressive Bale but Strachan insists his preparations will involve more than simply trying to nullify the threat posed by the free-scoring Tottenham man.
He said: "Wales have good players but I go to my bed at night with the knowledge that I'll be training good players, I will be picking good players.
"When I come to training, I will be doing a certain amount on how we stop Wales playing but I'll be doing a lot more on how Scotland have got to play and how to give Wales problems.
"What I'm looking for is, when the players line up in the tunnel, they look about their team and say, 'I'm glad you're in my side tonight. I'm glad you're with me'.
"That's what makes you feel better.
"Sometimes what's across the other side of the tunnel doesn't make a difference, it's about how you feel together as a group and how good you feel about each other.
"I know the players will be looking at each other and saying, 'I'm glad you're here'."
Bale stole the show the last time the two nations met when Wales secured a controversial 2-1 win in Cardiff in October.
Asked if Bale is even better this time around, Strachan added: "I really don't know. Has James Forrest got better since the last time we got together? Definitely.
"Is Shaun Maloney playing better? Definitely. Is Chris Burke playing better? Definitely.
"So I know that for a fact. I don't know for a fact how every Wales player is playing and are they better now than they were four weeks ago."
Strachan named a 28-man squad at Hampden today for the double-header, with Scotland set to travel to Serbia four days after hosting Wales.
He sprang a major surprise by calling up Brighton midfielder Liam Bridcutt, while Dundee United winger Gary Mackay-Steven and Peterborough forward George Boyd - currently on loan at Hull - were also named in the squad for the first time.
The inclusion of Bridcutt, who qualifies through his Scottish grandfather, is subject to Scottish Football Association paperwork being completed.
Both Strachan and assistant Mark McGhee, a former Brighton manager, have watched him closely.
Strachan said: "Mark McGhee, who lives in the Brighton area, has seen a lot of Liam and he did his homework into the type of guy Liam was and did he want to play for Scotland.
"In central midfield, we have lost Scott Brown and Darren Fletcher so there is a hole and hopefully Liam can help to fill that hole."
Former Scotland Under-21 international Mackay-Steven has returned to top form for United in recent weeks after an injury-hit first half of the season.
Strachan said: "I've seen him a couple of times recently and he makes an impression on the game, that's for sure.
"He wants to do something that's positive every time he picks the ball up and that's the kind of thing I'm looking for."
Boyd has scored two goals in three games for Hull since his loan move, which followed an aborted attempt by former Scotland manager Alex McLeish to sign the player during his short reign at Nottingham Forest.
Strachan said: "He is an elegant player, a good passer and he scores a fair amount of goals for an attacking midfield player.
"I spoke to Darren Ferguson about him and Darren says he is the best player he's worked with. (Hull manager) Steve Bruce said at the weekend that he didn't realise how good he was.
"I tried to sign him at Middlesbrough and it didn't materialise. Alex McLeish tried to sign him at Notts Forest and it didn't materialise.
"If you look at the people he has got testimonials from, it looks not too bad."
Rangers defender Lee Wallace failed to retain his place in the squad, while Strachan revealed in-form Hibernian striker Leigh Griffiths just missed out.
He said: "When we were putting the squad together on Monday, his name was mentioned a lot and he finds himself very unlucky not to be in this squad.
"I picked a squad that I know will do a great job in the next two games.
"There was a point where I had to perm two from three and he was in that three so he is unfortunate at this time because other players are playing very well as well."
Scotland squad to face Wales on March 22 and Serbia on March 26 in World Cup qualifiers:
Gilks (Blackpool), Marshall (Cardiff), McGregor (Besiktas); Berra (Wolves), Caldwell (Wigan), Fox (Southampton), Hanley (Blackburn), Hutton (Real Mallorca), Martin (Norwich), Mulgrew (Celtic), Webster (Hearts); Adam (Stoke), Bridcutt (Brighton), Burke (Birmingham), Commons (Celtic), Dorrans (West Brom), Forrest (Celtic), Mackay-Steven (Dundee United), McArthur (Wigan), Morrison (West Brom), Snodgrass (Norwich); Boyd (Hull), Fletcher (Sunderland), McCormack (Leeds), Maloney (Wigan), Miller (Vancouver Whitecaps), Naismith (Everton), Rhodes (Blackburn).
