Matic left Premier League champions Chelsea to reunite with Jose Mourinho at Old Trafford in a deal reportedly worth £40 million.
The Serbia international has made an immediate impact in Manchester, producing a man-of-the-match display in last week's season-opening 4-0 rout of West Ham, and Robson praised the club's transfer business.
"To have signed Matic was a masterstroke for me," Robson told talkSPORT . "The signs there at the weekend were brilliant and I think he is going to be a great player for Manchester United over the next few years."
United will look to make it back-to-back wins to start the Premier League campaign when they travel to Swansea City on Saturday.
Fellow recruit Romelu Lukaku impressed with a brace against West Ham, while Paul Pogba, Henrikh Mkhitaryan and Eric Bailly – signed by Mourinho last season – were also influential.
"You look at the squad in depth and we have got power and pace as well as the quality," Robson added. "We are going forward and we are going forward in a real good way.
"All of Mourinho's signings have been very good and they have definitely strengthened us.
"Winning a couple of competitions last season gives the players loads of confidence and you can see the way they were bonding together on the tour to America that the lads get on really well together.
"There is a real good spirit amongst the players at this moment in time."