United secured a £52 million deal to land the 25-year-old from Shakhtar Donetsk earlier this month and the midfielder will link up with his teammates after Brazils World Cup campaign.
Fred was also on Manchester Citys shortlist and Pep Guardiola was keen to sign the Brazilian in the January transfer window.
But United managed to beat their rivals to the transfer and Fred will be partnering Matic in central midfield next season.
Matic met up with Fred after Brazil beat Serbia on Wednesday evening and welcomed Uniteds new arrival by giving him his shirt.
And when asked about Freds move to United after Serbias 2-0 defeat, Matic was buoyed by the prospect of playing alongside the Brazilian at Old Trafford.
I spoke to him after the game, he is a great player, he will bring quality to our team, said Matic.
We will see. I think well understand each other very well.
More: Manchester United FC