The money received by Doncaster makes it a record sale by the Yorkshire side.
Wellens told BBC Radio Sheffield: "I'm pleased it's gone through but it took quite a while.
"They're a big club with a big fan base and they want to get back in the Premier League.
"I wasn't looking to leave, but as soon as I heard a club like Leicester were willing to pay the money Doncaster wanted I went down and spoke to them, and couldn't really say no to be honest," Wellens added.
"It was just a case of at my age and in my situation it was a good move. I feel the fee they got for me is good as well."