The retired Scotland international was a free agent, having turned down a new deal at Luton Town at the end of last season, and has been weighing up his options over the summer, with Motherwell the latest side to be linked with the player.
Fir Park boss Stevie Hammell offered the 35-year-old a deal last month but the former West Ham midfielder refused to commit and has since been considering other offers since the transfer window closed last week.
Hearts have now stepped in and completed a deal, adding him to their squad ahead of their Conference League group matches, which kick-off on Thursday with a home tie against Istanbul Başakşehir.
Snodgress, however, is unable to play in any European ties for Hearts until the last 16 stage at the earliest due to the squad submission deadline for the group stages having already passed.
The Gorgie side have enjoyed success in the past with free agents, picking up Stephen Kingsley in 2020 and Barrie McKay in 2021, and both have gone on to become key players in maroon.
With that in mind, manager Robbie Neilson had stipulated a willingness to show patience and wait to see what gems were available after the window closed and although he added striker Stephen Humphreys on transfer deadline day, he has now moved to further strengthen his squad as the games come at his men thick and fast.
Looking for proven quality and experience in the attacking ranks, Snodgrass, who has been capped 28 times, fills the creative void left by Northern Ireland international Liam Boyce, who has been ruled out with cruciate ligament damage for up to another eight months.
“I’m really pleased that we’ve been able to bring Robert in for the season,” Neilson said.
“He’s got a huge amount of experience and has played at the highest level, both domestically and for his country.
“The knowledge he’ll bring to the squad, as well as his qualities on the pitch, will be invaluable and I’m looking forward to working with him.”
Sporting Director Joe Savage added: “Robert had offers elsewhere but after we spoke to him he decided that Hearts was the place to be, and we’re delighted that he’s here.
“He’s a household name in Scotland and has spent years playing at the top level in England, so it was too good an opportunity to pass up and as we’ve stated in the past, we’ll always bring in quality over quantity and wait for the right moment to do so.
“Robert coming in gives Robbie more options and squad depth for our domestic campaign, which is hugely important for us.
“We’ve got some really talented young players at this club and I hope that they are able to learn from Robert because he really does have a lot to offer.”