Marshall, with 47 caps to his name joins on a two-year pre-contract deal which begins in July.
The move has been rumoured for several weeks but Lee Johnson was pleased to have the goalkeeper sign.
He said: “I’d like to offer David a very warm welcome. He’s an excellent goalkeeper and actually a player that I’ve tried to sign before.
“His experience will be invaluable for us both on and off the pitch. It’s vital that our senior players aren’t just great characters, but also help us set the standard around the training ground and on matchdays.
“He is a fantastic addition to this squad, and I’m looking forward to working with him.”
The goalkeeper, a national hero after his penalty shoot-out heroics in Serbia which sent Scotland to Euro 2020, came through the ranks at Celtic and rose to prominence with performances against Barcelona as a teenager under Martin O’Neill in the Champions League of 2004/05.
Among the benefits of recruiting a goalkeeper of the 37-year-old’s experience, is the 550-plus game knowledge he can pass on to younger goalkeepers around him and Hibs’ head of recruitment, Ian Gordon, added on the club’s website: “We have a young, talented, ambitious team, but we know that if we want to be successful, we need to have a good balance in terms of experience and leadership, and David Marshall fits that mould perfectly.
“He is a real professional, who will push on the other ‘keepers and really help accelerate the development of our younger goalkeepers like Murray Johnson.”