He is now set to be rewarded for helping the club retain the SPL title by agreeing a new deal during the summer.
"My agent, Lou Sticca, flew from Australia for talks with Peter Lawwell last week," said McDonald.
"He told me that things had gone well, but I said I didn't want to know any of the details.
"I wanted to concentrate on our match against Dundee United and winning the title. Everything else could wait.
"Now that we've won it, it's the most incredible feeling I've experienced, and I want more of this.
"That's why I'm so thrilled at the prospect of signing a new deal and making sure I've got a few more years of winning trophies for Celtic in front of me."