The 6 feet, 7 inches (2 metres) tall left-armer replaces Matthew Potts for the third Test at The Oval starting on Friday.
England are 2-0 up in the series after a 3-0 clean sweep against the West Indies in July.
The 20-year-old Hull, who only made his first-class debut last year has taken just 16 wickets in 10 matches for Leicestershire who play in the second division of the County Championship.
This season he has taken just two wickets in the championship at the strikingly unimpressive average of 182.50.
But England have made a habit of taking a punt on young talent since head coach Brendon McCullum and captain Ben Stokes took charge, throwing Rehan Ahmed and Shoaib Bashir in with even fewer games under their belts and promoting Jamie Smith and Gus Atkinson ahead of more established campaigners.
Ollie Pope, who this week completes a three-game run as stand-in captain for the injured Ben Stokes, is looking forward to seeing Hull in action.
"When you're six foot seven, you can get it down, sort of pushing up to the 85-90 (miles-per-hour) mark and with a bit of swing with the left arm angle, there's a lot to like about it," he said.
"We're 2-0 up, but I think he's obviously still going to have those nerves coming in. But we know what he can do moving forward. And it's a great week for him to come in, learn a little bit and show off exactly what he can do."
Pope said Hull would give Sri Lanka something new to think about after England played four right-arm seamers for the first two games of the series.
"It's a point of difference and he's got some good pace when he's clicking in the nets," said the stand-in skipper.
"The numbers sometimes speak for themselves but there's obviously a bigger picture with some of the guys.
"There's a little bit more to the numbers and I think it's credit to the way the guys have gone about it, the boldness from Brendon and Ben to get these guys in the squad at such a young age.
"Why not get him in? This is a great opportunity for him, you can show exactly what you can do on the international stage."
England squad:
Dan Lawrence, Ben Duckett, Ollie Pope (capt), Joe Root, Harry Brook, Jamie Smith (wkt), Chris Woakes, Gus Atkinson, Olly Stone, Josh Hull, Shoaib Bashir
