Vidic departed for Inter at the end of last season after his contract expired, vacating the captain's armband at Old Trafford.
And the club confirmed on Tuesday that Rooney was the man coach Louis van Gaal had chosen to lead them into the new season, with Darren Fletcher as his deputy.
"For me it's always very important the choice of captain," said Van Gaal. "Wayne has shown a great attitude towards everything he does.
"I have been very impressed by his professionalism and his attitude to training and to my philosophy.
"He is a great inspiration to the younger members of the team and I believe he will put his heart and soul into his captaincy role."
Rooney captained United to a 2-1 friendly victory over Valencia on Tuesday and declared his pride at landing his new role.
"It is a huge honour for me – and for my family – to be named captain of this great club," he added. "It is a role I will perform with great pride.
"Team spirit has always been very high in our dressing room and I am very grateful to the manager for the faith he has shown in me.
"I look forward to leading the team out on Saturday at our first match of the new season."
United begin their Premier League campaign at home to Swansea City on Saturday.
