Evans, who was released by Blackburn Rovers in the summer, becomes the club’s second summer signing after Alex Pritchard joined the Black Cats last week.
The midfielder had previously been linked with a Championship move this summer.
Having started his career at Manchester United – alongside his older brother Jonny, who also spent time with Sunderland – the 30-year-old spent time on loan with Carlisle United and Hull City before then making a permanent move to Humberside.
A move to Blackburn then followed, where Evans was instrumental in helping the side gain promotion from League One 2018.
An established international with 65 caps to his name, the midfielder will help to fill the void left by the departures of Max Power, Josh Scowen, Grant Leadbitter and George Dobson this summer.
And Johnson has revealed the key role he sees Evans playing in the engine room this season.
“Corry is an established international and he comes in to anchor, and be the glue in, our midfield,” he said, speaking to safc.com.
"He carries out a special role and it’s something that we’ve needed – we obviously lost a very good one in Grant Leadbitter, but we have been able to replace him with a long-standing international.
"He will make other players around him better and his maturity, experience and game-understanding will really set him apart.”
Evans, meanwhile, says that Johnson's sales pitch coupled with the impressive facilities at the Academy of Light convinced him to make the move to Wearside.
“I’m delighted to have joined Sunderland,” added the midfielder.
"I spoke to the Head Coach and was impressed with the way he discussed his style of play and coming to look at the training ground convinced me that this was a great place to play football.
"From experience, I know that League One isn’t easy to get out of – it’s all about consistency and getting it right, so I’m excited to get going.”