The Edinburgh club are managed by former Wanderers striker Mixu Paatelainen, who like Jaaskelainen hails from Finland.
The 34-year-old is being rewarded for his long service. He has made 425 appearances after arriving from VPS Vaasa in November 1997.
Jaaskelainen told www.bwfc.co.uk: "I am extremely proud of what I have achieved at Bolton. To represent the club for as long as I have done is tremendous.
"It is great my fellow countryman will be bringing his team to Bolton. It should be a good curtain-raiser to the new season."