Supporters of both clubs were concerned about transportation for the FA Cup final if the London Underground was fully or partially closed.
However, tube workers have reported reached an agreement after the London Underground moved away from pans to cut funding for train inspections and preparation.
Rail, Maritime and Transport Union general secretary Mick Cash said: "It is a massive achievement for this union to overturn the planned cuts to Tube train inspections and preparation but the campaign doesn't stop here.
"We now expect London Underground to reverse the planned cuts to jobs under their 'transformation' programme and give us an assurance that there will be no further attacks on our members, their working conditions and the safety culture on the Tube network.
"Our action this week is suspended but RMT remains vigilant and will have no hesitation in taking whatever steps are required to block cuts and their consequences wherever and whenever they may emerge."