Coventry's promotion was confirmed after Friday night's draw at Blackburn Rovers.
Redknapp wrote for The Sun: "Frank Lampard to take Coventry back into the Premier League is a massive achievement.
"And I’m not just saying that because he’s my nephew.
"I must be honest, at the start of the season, Coventry wouldn’t have been on my radar as one of the teams to go up, even though they had a great run last year.
"I was looking at clubs like Ipswich, Middlesbrough, Southampton.
"From my time at Portsmouth I know how hard it is to come through a tough 46-game season, competing against teams with parachute payments.
"Frank has done brilliantly and all credit to him.
"After having a couple of setbacks in his managerial career, he did not have to take the Coventry job.
"It was a big decision, especially after Mark Robins did so well there for a while and was so popular.
"Frank doesn’t need to go to work, that’s for sure. He could have gone off and played golf every day, if he wanted to.
"He could have easily sat down with me and said, ‘I’m going to do a little TV for the next 10 years’.
"But he didn’t. He’s put himself right back in the frame again because he has the same passion he had as a player."