The Argentina international winger completed his British-record transfer from Real Madrid on Tuesday, taking the club's outlay this year to over £130 million.
The Red Devils boss is thrilled to have secured the midfielder's services, telling the club's official website: "Angel is a world-class midfielder ... there's no doubting his immense natural talent.
"He is a tremendously fast and an incisive left-footed player who puts fear into the most accomplished defence.
"His dribbling skills and ability to beat opponents are a joy to watch. He's an excellent addition."
Di Maria claimed upon sealing his move that United were the only club for whom he would have left Madrid, where he was pushed down the pecking order by the arrivals of Toni Kroos and James Rodriguez.