Fletcher came on as a 70th-minute substitute in the 3-0 victory over Aston Villa, his first appearance since Boxing Day last year, after battling a chronic bowel condition. He had been forced to take an extended absence from the game when he was first diagnosed with ulcerative colitis in 2011, playing just 13 times last season including two games for Scotland.
The midfielder is yet to feature for the national team since Strachan's appointment at the start of this year, but the manager admitted news of Fletcher's return had "really cheered me up".
"Darren's probably had all sorts of different Christmas presents over the years since he was a wee boy," said Strachan, "but I think this will go down as his best gift ever - to get back playing football. It's fantastic.
"I was asked [last week] about Manchester United and how they were doing, and what they were missing. I think it could be him. People maybe took it for granted before his illness, but any time they were in trouble at United, he played. In all the big games, he played.
"I actually see him as being a left-over from that class of '92. I know he wasn't part of that group, but he has that in him, where winning is the most important thing."
Strachan praised the work of the medical staff who have helped Fletcher back to full fitness, as well as the player's support network of family and friends.
"A lot of people have helped him out during his battle," he added. "He's had friends and family who'll have been there for him as well as the medical people involved in the surgery. It's like anything in life, it's the people round about you who make a difference and help to make you successful. In saying that, though, he's had to work to get back and I'm delighted for him."
Fletcher's last appearance for Scotland came in the 2-0 loss away to Belgium in October 2012, but Strachan doesn't want to rush his return. "We'll just see how it goes for the next couple of months. We'll let him enjoy this and get in touch with him to tell him how happy we are for him.
"For us, he adds to what we have in the middle of the park, which is absolutely fantastic. But we'll let him take his time. I think that's what he wants as well. He's a top player, though. He moves people around about him. As he plays, he organises, and not every player can do that."