The 39-year-old, who joined the Hammers in 2012 from Bolton, is hoping to challenge for a first-team place after being dislodged last season by Spanish keeper Adrian.
"I'm delighted to sign for another season and I'm really looking forward to it," Jaaskelainen told the club's official website.
"Hopefully I can put in a proper challenge to get a starting place again. Physically, I feel good now and I felt good last season so I hope I can carry on from there and play football.
"You never know what is going to happen next season, but the only thing in my mind is to get myself ready to play.
"I am looking forward so that when that next chance comes, I will be in the right shape and right frame of mind to take it. That's all I'm thinking about now.
"Obviously we all know that, whoever is in the squad, we all want to fight for that starting place, so let's see. We're all looking forward to next season."
The former Finland international wants the Hammers to avoid last season's flirtation with relegation.
"Last season was a bit disappointing as in the early part things didn't really work out because we didn't really score enough goals and then we got injury problems.
"If you look at it, we finished 13th, having had a difficult season, so it's not the end of the world. We have to make sure we're ready for this coming season.
"In our first season back in the Premier League, we started well, but last season we didn't get those points on the board early on and that's what created the pressure and all the injuries just made it worse.
"We have to make sure we're ready for this coming season so we can start well."