The 29-year-old, who has played in three friendlies for the Seasiders, has put pen to paper on a two-year contract at Bloomfield Road, with the option of a third, following his release from Dundee.
“The club was up in Scotland last week and I managed to spend a full week training with the boys, playing a part in a couple of games,” McAlister told the club’s official website.
“I’m seeking a fresh challenge and thankfully I’ve been given the opportunity to come here. I’m really, really looking forward to getting started.
“I spoke to Kyle Letheren before I met up with the boys up in Scotland last week and he had nothing but good things to say about the whole place in general, from the manager, through to the squad and the stadium. That whetted my appetite a wee bit to try and get a deal here.”