The former Dynamo striker and Ukraine international was appointed as Oleg Blokhin's successor in April after the club suffered a string of poor results.
However, since then Dynamo have lost just once under the guidance of Rebrov, with the 39-year-old also guiding Dynamo to cup glory.
Rebrov's charges saw off Shakhtar Donetsk 2-1 in the final in Poltava on Thursday before rounding off their league campaign with victory over Zorya.
President Igor Surkis confirmed Rebrov's appointment on Sunday, having said previously he was pleased with the side's improvement over recent weeks.
Asked by the club's official website whether Rebrov's appointment had reenergised the club following their cup win, he said: "There's no doubt that it has.
"We didn't let Shakhtar create chances in the first half but we shouldn't fall into euphoria. We were just more motivated.
"Still I'm sure that Rebrov is on the right track."
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