The 29-year-old had long been linked with a move to the Walkers Stadium and the deal was finally done on Tuesday night for a fee which could be worth £1.2million.
Wellens told BBC Radio Sheffield: "My time at Doncaster has probably been the best two years of my career.
"We have had success and last year we finished 14th, which was a big success for us. To be honest, I am gutted. I didn't want to leave and I wasn't looking to leave but as soon as I learned that a club like Leicester were willing to come in and pay the money that Doncaster felt they would want for me - I went down and spoke to them and I couldn't really say no to be honest.
"I am going to miss playing for them. The way that Sean (O'Driscoll) had us playing makes us a good side and I love the way we played football and I am definitely going to miss that.
"I think that the move suits both parties. Sean can now go out and get some players in and he also gets me off of the wage bill. I get to move to a big club and, obviously, more money as well. I can now play in front of 25/30,000 fans every week."