The Dutchman was officially presented to the media on Thursday after the club finished seventh in the last campaign.
"It's the start of a new era for the club, with a new manager and players coming in," Mata told MUTV.
"I'm really happy with the manager's style of football and hopefully at the end of the season we can celebrate something, which would be amazing for him and for us."
"We're focused on improving and trying to learn from the manager, to play at our best level during the season. The main idea is to play as a team and compete for titles."
Van Gaal arrives at Old Trafford having won league titles with Ajax, AZ Alkmaar, Barcelona and Bayern Munich.
The 62-year-old also led the Netherlands to third place at the World Cup in Brazil.