Jaaskelainen, 37, is hoping his move to Upton Park can help extend his playing career.
"I was prepared to fight for my place and Bolton had offered me a two-year contract," said Jaaskelainen.
"I was very happy, though, when Sam said he wanted to sign me and I said to myself: 'Just do it' because I know the way he looks after his players. I know the way he looks at every detail in preparation to help get that extra edge.
"Hopefully, by coming to West Ham and playing under him, he will get two or three years more out of me. I'm happy here. The backroom staff are brilliant, I'm happy with the goalkeeping coach and the squad are good."