McManus joins an already growing Scottish contingent at the Riverside after Kris Boyd completed his move last week.
“It was something I thought long and hard about over the summer with the new manager coming in as well,” McManus told Boro’s official website.
“I have worked with Neil for a number of years and it was a really, really tough decision.
“I had a year left on my contract at Celtic, I had been there for 12 years and coming down here really opened my eyes to different things, not just on the football side of it, but the way you can live your life as well.
“It’s the hardest decision I have ever had to make in my career, leaving Celtic. I had 12 wonderful years there from a kid when I left school.
“I went full time in 1998, and it was a really, really hard thing for me to do, finally walking out of the door.
“Celtic will always be a part of me, it will always be my first love in football. But I am coming down here, it’s a fresh challenge and I am really looking forward to it.”