The player moved to Upton Park to reunite with former boss Allardyce on a free transfer last summer, after spending 15 years between the posts at Bolton.
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"It's sorted," Allardyce told reporters. "The option is linked into this year and kicked in with him completing the games.
"There is no doubt about the value of his signing."
In total Jaaskelainen has made 505 appearances in all competitions since moving to the UK in 1997, as well as representing his national team 56 times and being named Finnish Player of the Year in 2007.