Jaaskelainen was managed by Sam Allardyce for much of his time at the Reebok Stadium and had no hesitation in accepting the opportunity to work with him again.
"I'm absolutely delighted to be here under Big Sam again, having worked with him before for a few seasons," Jaaskelainen told West Ham's official website before jetting off with the rest of the squad on Monday morning for a pre-season training camp in Austria.
"It happened very quickly because when my agent said that West Ham were interested I told him to sort it straight away because I know how Big Sam works, how well he looks after the players and how good his backroom staff are. They were the factors behind why I wanted to come here.
"He brings certain routines and that makes it a lot easier."