"I know Scott from our time at The Hawthorns and have kept an eye on his career since then," said McInnes.
"He will complement our existing options - he has pace and strength and can play in a wide role if required."
Dobie was capped six times for Scotland under Berti Vogts and also spent time with Carlisle, Millwall and Nottingham Forrest.
I'm not a 20 or 30 goals a season type of striker but I know I can weigh in with my fair share
Scott Dobie
"I'm really looking forward to it," said Dobie.
"I've never played in the SPL but I have a lot of experience in England and I have faith in my own ability to get goals for St Johnstone."
"I'm not a 20 or 30 goals-a-season-type of striker but I know I can weigh in with my fair share.
"I'm just looking forward to getting started. I played alongside Jody Morris at Millwall and have come up against Michael Duberry a few times so I can't wait to meet up with them and the rest of lads."
Source: BBC Sport
Source: BBC Sport