The centre-back had already been out with a medial knee ligament injury earlier in the campaign before rupturing his Achilles tendon in the 1-0 win over Crystal Palace in January.
The 29-year-old, who is currently in talks over a new contract, then underwent an operation at the end of January before using a protective walking boot for several weeks as he stepped up his recovery.
Fortune has been continually working hard at Charlton's training ground to ensure he is ready for the new season and club physio Stuart Ayles is pleased with his progress.
He told the club's official website: "Jon's progressing well. He's now doing work outside and running with the ball.
"We still need to increase his strength and power. Hopefully, if things go to plan, he will be ready to join the boys for the start of pre-season."