Cellino's decision last week to restrict Leeds' away allocation to 2,000 tickets in protest at increased live coverage of the club's Sky Bet Championship matches was met by outrage among fans.
The Italian announced his decision after being informed of his second Football League ban, but backed down in the row following a meeting with supporters' group Leeds Fans Utd.
Leeds Fans Utd chief executive Dylan Thwaites said: "Our away support is second to none for their commitment to following the team all over the country.
"We hear the frustrations from supporters who have to miss games or pay extra money because of amended fixtures.
"We will all work together to come up with a solution that works for everyone."
Fellow fans' group Leeds United Supporters Trust said: "We welcome the decision made by the club to not take forward the proposal to limit how many away tickets the club will accept (and thus the opportunity for supporters to support the team).
"We also thank Leeds Fans United for using their good offices to persuade the club of the common sense of reversing that idea.
"The Trust thanks all fans who made their voice heard over the last few days on this issue."
Leeds will have featured in 10 live televised games before the turn of the year, prompting multiple fixture amendments and Cellino claimed the Football League and Sky had refused to acknowledge his complaint that the club was losing money as a result.
Cellino said: "We are frustrated by the fixture changes but we never intended to penalise our own supporters at away games - we have listened to their concerns and acted on them."