Di Maria completed a Premier League-record £59.7 million transfer to the Red Devils from Real Madrid last week, while Blind is expected to finalise his switch from Dutch champions Ajax on Monday.
And Mata is confident the incoming duo, who both starred at the World Cup, will boost a United side still without a win in a competitive game under new boss Louis van Gaal.
"As you read this, many things are happening before the transfer window expires today," Mata wrote on his personal blog. "Here I would like to welcome Di Maria and Blind to the club.
"I am sure these two players will give a lot to us and will strengthen the team. We already know what Angel is capable of, his ability and dribbling skills, and Daley has a great touch and is very intelligent, as he showed during the World Cup."
The Spain international also took the opportunity to praise departing midfielder Shinji Kagawa, who has returned to Borussia Dortmund after a disappointing two-year spell in English football.
"I would also like to wish all the best to Shinji Kagawa, a fantastic player but especially a great person," Mata added.
"It's been a pleasure to be his team-mate and I'm sure both Borussia Dortmund and fans everywhere will enjoy his football again."