Matic, 29, delivered a commanding display as the Red Devils romped to a 4-0 win over West Ham United on Sunday (13 August) and will hope to build on his impressive performance when the Red Devils face Swansea City on Saturday.
Many questioned Chelsea's decision to sanction Matic's £40m transfer to Manchester United. Members of the Blues hierarchy were seemingly fine to help a perceived rival for the Premier League title markedly strengthen their starting line-up, even though manager Antonio Conte was decidedly against the idea of allowing the Serbian midfielder to move to Old Trafford.
Conte's apparent irritation over Matic is not of any importance to Jose Mourinho's side, and Robson believes the former Chelsea anchorman has the capacity to replicate the success he enjoyed during his 13-year spell at Manchester United, during which he won two league titles and three FA Cups.
"To have signed [Nemanja] 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."
Matic's move to Old Trafford was preceded by the arrivals of Romelu Lukaku and Victor Lindelof, who have endured differing fortunes during the embryonic stages of their respective Manchester United careers. Former Chelsea prodigy Lukaku scored a brace on his Premier League debut for Mourinho's side against West Ham but Lindelof was left out of the matchday squad altogether as he bids to acclimatise to the rigours of English football.
Despite Lindelof's perceived struggles, Robson thinks all of Mourinho's recruits have gone some way to strengthening the EFL Cup and Europa League holders, who will be gunning for even greater success this time around.
"You look at the squad in depth and we have got power and pace as well as the quality," Robson said. "We are going forward and we are going forward in a real good way. All of [Jose] 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."
Mourinho is still searching for another player to round off his summer spending spree, but the Portuguese is reportedly set to miss out on Paris Saint-Germain defender Serge Aurier. Tottenham are believed to have reached an agreement with the €25m-rated Ivory Coast international over a move to north London, with his chances of game-time in the French capital substantially lowered by the arrival of Dani Alves.