The 32-year-old striker enjoyed a successful loan spell with Town at the end of last season until suffering the serious injury against Norwich in the Sky Bet Championship play-offs.
Varney, now a free agent after his contract with Blackburn expired, has undergone surgery and will now bid to get back to fitness and earn a permanent deal at Portman Road.
“The club have been great with me and I’m already working on my rehab, getting some treatment,” he told Town’s website.
“I just want to get back and play for Ipswich again as soon as possible now.
“I’m in good hands and I just want to pull that Ipswich shirt on again and repay all the players, staff and fans for their support.”