The former Red Devils manager wished the couple years of happiness in the short clip which was played at their wedding in France at the weekend.
Bryan Robson also sent a personal video for the bride and groom as they tied the knot.
A source from The Sun stated: A source said: "It was a beautiful day. No expense was spared.
"There were so many lovely touches - including the video messages from Sir Alex and Bryan Robson.
"Both of them wished the happy couple many years of happiness together. Tom Grennan then got up and sang his song Little Bit of Love.
"There were so many magical moments."