Since being appointed a year ago, ex-Salford City boss Alexander, 50, has transformed the playing squad, won three Manager of the Month awards and in 2021 accumulated a points tally of 59 which was only bettered in the calendar year by Rangers and Celtic.
McMahon told the club website: “We have been absolutely delighted with Graham’s contribution since joining our club 12 months ago and we are excited about what he is trying to build with us.
“He is talented, hard-working, dedicated and fully buys into the multifaceted role at Motherwell.
“The board will continue to back him to help us achieve our goals both on and off the pitch.”
Ahead of their scheduled return to Scottish Premiership duties at Ross County next Tuesday evening, Alexander statistically ranks near the top of the modern-day Motherwell bosses with a win percentage of 47.8% and a league points per game record of 1.55.
Meanwhile, First Minister Nicola Sturgeon confirmed on Tuesday that restrictions on crowd numbers at big events – including Scottish Premiership football games – would be lifted from next Monday, January 17.
Due to the rise of the Omicron variant of coronavirus, a 500-people limit had been placed on attendances at outdoor events in Scotland to help curb its spread, but thousands of fans will now be able to return to games.