Football's world and European governing bodies said they were satisfied progress had been made to end political interference in the Ukraine Football Federation (FFU), which had faced a February 4 deadline.
"The latest developments are seen positively and... this is an important step forward to unify and strengthen football in Ukraine," FIFA and UEFA said in a joint statement.
"Under these circumstances, FIFA and UEFA are convinced that there will be no need to suspend the FFU, but they will continue to monitor the situation over the next few weeks to have the confirmation that the situation in Ukrainian football is definitely stabilised."
FIFA and UEFA do not tolerate outside interference in member federations and the European body said last month that Ukraine, due to co-host the tournament with neighbours Poland, could not stage the event if suspended.
A ban would also have meant the three Ukrainian clubs still involved in European competition would have forfeited their matches.
Shakhtar Donetsk have been drawn against AS Roma in the last 16 of the Champions League while Dynamo Kiev face Besiktas and Metalist Kharkiv meet Bayer Leverkusen in the knockout stages of the Europa League
UEFA general secretary Gianni Infantino said last month that FIFA and UEFA had received documents showing that some state and regional authorities were putting pressure on delegates.
FIFA warned the FFU against trying to dismiss its president Hrigory Surkis before the end of his current term, which expires after Euro 2012.
Several FFU members tried unsuccessfully in December to sack Surkis who has been accused by some fans of favouring Dynamo Kiev, a team run by his brother Ihor.
The football scene in Ukraine reflects competing interests among major oligarchs and local media reports said several key figures in the political establishment, including Euro 2012 minister Borys Kolesnikov, wanted Surkis out.
Ukraine's preparations for the event have also been dogged by delays in building stadiums and other infrastructure, earning the warnings from UEFA.
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