The 2012 Tour de France and Olympic time-trial champion took the leader's gold jersey as the first Team Sky rider to win their home tour as Mark Cavendish (Omega Pharma-QuickStep) triumphed on Whitehall.
Wiggins then turned his attentions to Wednesday's Road World Championships time trial in Italy.
"The feeling at the moment is more just relief than anything else," said Wiggins, after his first stage-race triumph since the 2012 Tour de France. "I said I wanted to win it. It is pressure for the whole week. Until you cross the line you just don't know. It's all right to think it's a bit of a ceremony round London, but it certainly isn't. You cross the line, you're pumped up. It's relief that you've finished and fulfilled it for your team and your team-mates.
"From tomorrow morning my thoughts turn to the World Championships and this will probably be forgotten. It's a bit like the Tour with the Olympics. Win the Tour one day, the next day you're thinking about the Olympics."
Wiggins, who had taken the race lead with victory in Tuesday's time trial at Knowsley Safari Park, defended it with his Team Sky squad until the end.
However, he feared a crash and a split in the peloton on the last of the 10 8.8km laps could grant Martin Elmiger a chance to take the title.
In the end IAM Cycling's Swiss rider had to be content with second place, 26 seconds behind, while Simon Yates of the Great Britain under-23 team finished third overall. Wiggins praised the crowd support throughout the eight-day event, which began in Peebles last Saturday, describing it as "overwhelming at times" as he bounced back from a troubled year in which he withdrew from the Giro d'Italia and missed the defence of his Tour de France title.
"There was an element of going through the motions in all the races early in the season," added Wiggins, the second British winner of the race after Jonathan Tiernan-Locke 12 months ago.
"I came out this week with the commitment that I showed last year," he continued. "I crashed on day two, was straight up and straight back in the bunch, unfazed by it. That was a sign that I was back to where I was last year, more than fitness levels and what numbers say. It's nice to be able to come to perform to your potential and please everybody. Everyone goes home happy."
Cavendish triumphed after a near-perfect lead-out from Omega Pharma-QuickStep team-mate Alessandro Petacchi for his third win of the 2013 race and record 10th in all. Sam Bennett (An Post Chain Reaction) was second, with Elia Viviani (Cannondale) third.
Cavendish, who won the concluding stage of the Tour of Britain for a third successive year, said: "It's been incredible, to be able to win the stage again in London."
He also paid tribute to Petacchi, a one-time rival, now key ally. "His road sense is like something I've never seen before," the Manxman said."He's super smooth, super intelligent, super calm. He keeps me calm. I haven't had this since I worked with (Mark) Renshaw and it's exactly the same with Alessandro."