Labour's Rutherglen MSP, James Kelly, said Celtic's supporters' groups deserved the credit for raising the issue at the club's AGMs.
Celtic announced in its annual report that it had implemented a minimum rate of Â£8.25 per hour from 1 July 2016.
This is in line with the voluntary living wage rate.
Mr Kelly said: "This is good news that Celtic Football Club are now paying the National Living Wage to all its staff.
"A lot of credit for this goes to the Celtic Trust and other supporters' groups for continually raising the issue at the past two AGMs".
The club had previously said that Mr Kelly, who is a Celtic fan, had "no knowledge of the workings of Celtic," and that he was using the issue for his own political purposes.
Celtic chief executive Peter Lawwell had also said that the club were being used by politicians over the living wage campaign.
But supporters' groups campaigned for the club to review its pay structure and pay the Living Wage rate.
Heart of Midlothian were the first Scottish club to adopt the National Living Wage and remain the only club in Scotland to be accredited by the National Living Wage Foundation.
An MSP who criticised Celtic for failing to pay the National Living Wage has welcomed the news that the club are now paying the minimum rate.