The central midfielder joined from Chelsea for an estimated £35 million and has had an immediate impact at Old Trafford.
Savage described the Serbian national, 29, as a "wonderful player" and credits him for Paul Pogba's recent performances.
"The more and more I look at it, it looks like a bargain," he told Goal. "Considering his experience and what he’s won in the game.
"I think the best piece of business in the window is Matic to Manchester United. That has allowed Pogba to go and produce the displays he’s doing.
"United to get Matic to allow Pogba to play as well as he’s playing is a stroke of genius."
Savage is baffled as to why current Premier League champions Chelsea allowed the star midfielder leave for their rivals.
"I’ve got no idea at all," the 42-year-old added. "You can see what he’s added to Manchester United already. He’s a wonderful player so I’m surprised Chelsea let him go."
Pogba's hamstring injury will mean Jose Mourinho will make changes to his starting XI versus Everton on Sunday, with Ander Herrera, Michael Carrick and Marouane Fellaini all potential replacements.
Robbie Savage is taking part in the 2017 EE Wembley Cup final at Wembley Stadium connected by EE on Saturday, October 7.
To view the latest episode of the Wembley Cup online series and purchase tickets for the live final click here.