Bougherra saw red in last week's 2-1 win over Aberdeen but had it downgraded to a yellow by a Scottish Football Association review panel.
He will thus be available to travel to Tannadice, where victory for Rangers would secure their first Scottish Premier League title in four years.
Aberdeen's appeal against the dismissal of Charlie Mulgrew in the same game was also addressed by the review panel, which met on Friday morning.
The former Celtic player had his red card reduced to a yellow and will be free to play against Hibernian at Pittodrie.
Rangers striker Kyle Lafferty, who was fined by the Ibrox club for play-acting in the incident which saw Mulgrew sent off, will have to defend an "alleged act of simulation" by the SFA's disciplinary committee after the review panel decided he had a case to answer.
For the sending-offs of Bougherra and Mulgrew, referee Stuart Dougal issued red cards on the advice of his assistant, Graham Chambers, but it was the referee who was asked by the SFA to reconsider the decisions after both clubs lodged appeals.
Meanwhile, Celtic defender Glenn Loovens will also face the disciplinary committee as will team-mate Scott McDonald.
Loovens was reported to the panel over a challenge on Rangers midfielder Maurice Edu during the Old Firm derby at Ibrox on May 9.
McDonald was referred by Dougal after the referee examined TV footage of his tackle on Dundee United defender Lee Wilkie three days later.
The disciplinary committee will not meet until the summer and any potential suspension would take effect next season.
Consequently, both Celtic players will be free to face Hearts on Sunday, while Lafferty is available for Rangers' trip to Tannadice.
Rangers 8/15, Draw 11/4, Dundee Utd 6/1