A season ticket will now ensure a seat at all home league and cup games.
The club has also dropped its "One Year Only" ticket and promised to be more transparent in its dealings with fans.
"This is a significant victory for supporters," said Duncan Drasdo, the chief executive of the Manchester United Supporters Trust (MUST).
The OFT started its investigation into the Premier League leaders' ticketing practices last December following a complaint from MUST, which was supported in its action by national fans' groups the Football Supporters' Federation and Supporters Direct.
United, which recently announced debts of £750m largely related to the purchase of the club by Malcolm Glazer in 2005, denied its terms and conditions were unfair but told the OFT it would implement the changes the consumer watchdog flagged up in time for next season.
Among those changes are pledges to provide clearer information on when, where and why season ticket holders are relocated for cup games, more information on the potential cost of long cup runs and a clearer appeal process for disputes over season-ticket cancellations because of non-payment for cup games.
Armed with this initial victory we now hope we can secure a fairer deal for all fans.
This last issue was raised by a number of MUST's 35,000 members, some of whom had their season tickets automatically cancelled when automatic payments for cup games failed to go through.
MUST actually asked the government agency to look into three areas of United's ticketing policy but the OFT opted to only pursue the "terms and conditions" claims, saying a wider probe would have been too expensive.
This means Manchester United, the world's second-richest football club in terms of revenue, can continue their controversial Automatic Cup Scheme (ACS), which means season ticket holders are required to purchase tickets for cup games, by automatic direct debit, whether they want them or not.
The club, which has enjoyed considerable success in recent years, did make one concession to fans this season - exempting Carling Cup games from the ACS - but has made it clear it intends to continue with the scheme in the future.
The Club World Cup holders have, however, agreed to guarantee all season ticket holders a seat for every home cup tie. Last season, some holders of the "One Year Only" ticket did not get tickets for the most attractive cup ties.
"We are very pleased a season ticket will continue to include (European and FA) cup matches," said Manchester United's chief operating officer Michael Bollingbroke.
Glazer borrowed heavily to buy Man Utd, saddling the club with huge debts
"That is central to our strategy and we have made the necessary changes for next season to avoid the situation where holders of some season tickets were not guaranteed tickets for some cup games.
"While the number potentially affected was small, we accept all season tickets should come with that guarantee in future."
But MUST still wants the OFT to investigate the ACS under competition law, as well as looking into ticket price increases since the Glazer family took over.
A spokesman for MUST told BBC Sport that season ticket prices have risen by 50-60% since 2005, although he admitted season ticket holders get more games than before.
But he also said the OFT's first foray into United's ticketing practices should act as a "springboard" for further action and represented a "major step for a club that rarely listens to its fans".
Drasdo added that experts consulted by MUST are certain that the ACS, the price increases and other "unfair practices" constitute an "abuse of a dominant market position".
"The OFT has, until now, not agreed to consider this under competition law due to resource implications," he said.
"But armed with this initial victory we now hope, with the further support of MPs from all parties and fans' organisations representing many clubs, we can persuade the OFT as to the merits of such an investigation and together secure a fairer deal for all fans."
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Its such a disgrace a club can automatically cancel someones season ticket if they dont buy cup tickets. £750m debt...No wonder they cant afford Tevez.
Glazer is fucking the club up, putting so much pressure on them being succssful or else they will be in massive financial trouble. They are coping ok now but when Taggart leaves they could be in a lot of trouble.
I hope the fans enjoyed paying over £100 to go watch the reserves on Sunday.
I know i will get shit for posting this but im sure the majority of U*d fans on here know im not a bitter blue, the fact is i think this is a disgrace and i would post this if it was another club in the same position.