Ince, who had been in talks with a number of Premier League clubs, has joined on a loan deal until the end of the season, with Palace's Stephen Dobbie returning to Bloomfield Road on a temporary basis.
Ince's father and former manager at Blackpool, Paul, told BBC Radio 5 Live: "I feel like Steve Parish is my wife, the amount of time I've spent with him today but we got there in the end.
"Other clubs wanted a permanent deal but we felt that wasn't right - we wanted to take a loan deal and see what the options are at the end of the season.
"Steve Parish has been fantastic and I'd like to thank Blackpool chairman Karl Oyston because he's played a massive part in getting this over the line.
"The only ones who could take Thomas were Palace and Swansea. I had a good conversation with [Swansea chairman] Huw Jenkins but we felt that Tony Pulis sold the club to Thomas and that he'd be part of the club and play games.
"He'll have that opportunity to show what he can do under Tony Pulis."
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