The 31-year-old has agreed a two-year deal at McDiarmid Park which starts on July 1 and he moves on after two seasons in Lanarkshire.
Although not a regular starter for Motherwell last season, Sutton still netted 13 goals including the clincher in their 3-0 Premiership play-off final second leg win against Rangers.
Having scored 22 times in 2013/14, the English forward will add much-needed firepower to Tommy Wright’s team.
Although St Johnstone finished fourth in the Premiership and qualified for the Europa League, they scored just 34 goals in 38 games.
Sutton could move earlier if a release from his contract with Motherwell can be negotiated and Saints will be keen to get him in their squad as quickly as possible.
Wright’s team play their first continental game on July 2 and will find out their opponents in the opening qualifying round next Monday.
Sutton admits European football was an attraction for him and said: “I’m really happy. The club did really well last year and hopefully I can be part of something good going forward.
“I’ve been fortunate enough to play in Europe a few times with Motherwell and Hearts and if we could get to the group stage that would be brilliant but that’s a long way away.
“The boys are a very good team and I’m looking forward to being a part of that. The manager was a big part in me signing and he seemed very keen from the outset to bring me in.
“There were a couple of other teams who were interested but he told me about his vision of how he thinks the club could get better.
“He seemed very enthusiastic about what the future could hold here and it would be great to be a part of that.”