The 30-year-old, who was recently on loan with Wigan, was released by Wolves at the end of the campaign and moves to the Shakers with a decent goalscoring record in the third tier.
Clarke has been prolific at that level for Southend, Chesterfield, Scunthorpe and Coventry, and Bury will be banking on him regularly weighing in with goals at the JD Stadium too.
“I am delighted as a manager/coach to be working with Leon Clarke next season and beyond,” said Shakers boss David Flitcroft.
“The club, chairman and management team have been working tirelessly for the last three weeks to capture the signature of Leon. When we found out a player of his ability and quality was potentially available we had to do all that we could to secure his services.
“He is pure pedigree and has incredible goalscoring ability. He has the pace, power and intelligence to have a massive impact for us next season.
“Leon met up with the management team and chairman at Carrington to discuss the Bury project and our progression as a club, and loved the direction we were heading in.
“He has games on his CV, knowledge and understanding of higher leagues to help guide us in the next stage of our progression.
“The fact that he wants to play such a huge part in our next chapter speaks volumes for both the club and player. He wants to be part of our football family and the environment that we and the players have created, and we can offer Leon both.
“It is now up to us as a club to offer Leon a home and training environment where we can maximise his ability and that is what we will do as a club.”