The striker’s future had been in doubt but chairman Roland Wycherley has made extra funds available to boss Micky Mellon.
Akpa Akpro helped Shrewsbury to promotion from Sky Bet League 2 last season, scoring nine goals, and had been training with the club this summer.
Jermaine Grandison has also been offered a new deal and is considering the contract ahead of Saturday’s Sky Bet League 1 visit of Millwall.
Boss Mellon told the Shropshire Star: “The only reason we have been able to make them offers is because the chairman has dug into his own pocket and tried to make the two deals happen.
“We are very, very grateful for that. He has dug into his own bank account, if you like and made the funds available to get these two players.”