Sangakkara, among the greatest batsman to have played the game, signed a two-year deal at The Oval with the option of an extra season. He will arrive for a "substantial part" of the 2015 season and Stewart is expecting a big impact.
"To have someone of his standing in the county game is great for Surrey and county cricket," Stewart told Surrey TV. "County cricket seems to take a few knocks but if the No. 1 Test player in the world wants to come and play then you've got a pretty good competition.
"We've been in discussions for a long time. He made it clear that he wanted to come and play at The Oval and now we've signed a contract and look forward to welcoming him."
Sangakkara is still to decide on his international future but is set to play a big part for Surrey over the next two seasons. Stewart has no doubts that he will play a significant role for the club, particularly as they attempt to gain promotion back to Division One of the County Championship.
"We're going to have to wait until the mid-to the back-end of February to confirm the exact dates of when he can join us but we're confident of seeing a substantial part of the season with Sangakkara.
"We're just waiting but I'm happy to wait for the calibre of player we're getting and the personality and character that he is. We've always tried to sign good players and good characters as well."
Sangakkara showed his retains all of his ability in Test cricket with his 11th double-century in New Zealand in Wellington. He is now second only to Sir Don Bradman for most Test double-centuries and the lure of the record is making him reconsider his initial plan to retire from Test cricket this year - potentially limiting his availability for Surrey.
But when he does arrive at The Oval, Stewart is expecting his prolific scoring to continue.
"He's done it for a long time now," Stewart said. "I played against him. I've watched him. Obviously Graham Ford has coached him with Sri Lanka and has a very good relationship with him.
"We know what we're getting, that's so important: someone who can work with our players and develop them and hopefully turn into international cricketers too.
"It's not just come in and disappear. He sees this as a nice way to almost finish his career. But he's still hungry - you've seen that in his recent series against New Zealand. He never has enough runs. Batting here at The Oval on good surfaces I expect him to score a bucket load."