Doncaster have made forward Dany N'Guessan their sixth summer signing.
Shrewsbury have rejected an offer from Burnley for winger Josh Ginnelly.
The 31-year-old striker became Fleetwood manager Graham Alexander's second signing on Thursday after Newcastle United’s Adam Campbell put pen to paper on a 28-day loan earlier in the afternoon.
Speaking to the club’s official website, Dobbie said: “I met the manager recently and within 10-15 minutes of speaking to him I knew this was the place I wanted to come to.
"I’m delighted that it’s done and I’m just looking forward to the start of the season now.”
Dobbie, who also counts Swansea City among his former clubs, will go straight into Alexander’s League Two play-off winning squad for this weekend’s Sky Bet League One encounter against Crewe Alexandra at Highbury.
The Scotsman, who spent the majority of last season on loan at Blackpool, will be reunited with his former Bloomfield Road team-mates Stephen Crainey and Keith Southern during his season with the Cod Army.