McInnes is delighted with the capture of the 31-year-old striker who finished up his second spell at Carlisle last month.
"I know Scott from our time at The Hawthorns and have kept an eye on his career since then," he told the club's official website.
"He will complement our existing options - he has pace and strength, can play in a wide role if required and I am sure he will make an impact and hopefully enjoy his football at the club."
Dobie expressed his delighted with the move, saying: "I'm really looking forward to it.
"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."
"Derek has been a big influence on my decision to come to the club.
"He was the captain of West Brom when I was there and he was a model professional there and I learned a great deal from him.
"He seems to be equally thorough and professional as a manager and I am looking forwarding to learning from him."
Dobie moved quickly to stress that he is not a target-man striker in the mould of Kenny Deuchar.
The former Millwall and Nottingham Forest player, who gained six Scotland caps during the Bertie Vogts era but has been out of the picture since, said: "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've always been at my best when playing off a target man - I've done so alongside the likes of Danny Dichio and Jason Roberts - and can play that role if required but I enjoy playing wide and did so in over half of last season at Carlisle.
"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: Team Talk
Source: Team Talk