Reports had suggested Fellaini would be sold this month but unless that injury proves less serious than expected, that would now seem unlikely.
The club made the announcement in a regulatory filing and said the transfer is worth 20 million euros.
Manchester United will return to the top four this season but it is only Liverpool that can challenge for the title, according to former England striker Michael Owen.
With new investors to attract and a team in need of strengthening to appease disgruntled fans, it's a busy August at Manchester United.
United's 2-1 loss to Swansea proved that the 20-times English champions are still without the players required to bury the memory of last season's horror show.
Manager Van Gaal said his team need to learn to cope with pressure after they slumped to a 2-1 home defeat to Swansea City on the opening day of the EPL season.
Louis van Gaal made a losing start to his Premier League career with Manchester United suffering a 1-2 loss against Swansea City at Old Trafford.
Manager Van Gaal has urged Rooney not to let the burden of the club's captaincy weigh heavily on his shoulders.
Injury sustained by Luke Shaw was caused by too many training sessions from new manager van Gaal, former assistant coach Raymond Verheijen said.
For the second straight season, a new era at Manchester United begins with a Premier League opener against Swansea.
This will be the first time in 19 years that Manchester United will be involved in the second round of the competition.