Heavily criticised in an independent report published last month for organisational failures which "almost led to disaster", European football's governing body said its refund scheme would cover the entire Liverpool allocation of nearly 20,000, as well as supporters of Real and other spectators affected by the trouble outside the stadium.
"Refunds will be available to all fans... where the most difficult circumstances were reported," UEFA said, adding that all ticket-holders who did not enter the stadium by the originally scheduled kick-off time, or could not get in at all, would also receive a refund.
"Given these criteria, the special refund scheme covers all of the Liverpool FC ticket allocation for the final, i.e. 19,618 tickets."
Real's 1-0 win at France's national stadium on May 28 was overshadowed by events outside, with the kick-off delayed by 37 minutes as fans struggled to access the stadium after police funnelled them into overcrowded bottlenecks as they approached.
Police then fired tear gas towards thousands of supporters locked behind metal fences on the perimeter to the stadium.
UEFA tried to pin the blame on Liverpool fans arriving late despite thousands having been held for hours outside the stadium before kick-off.
A leading Liverpool fans' group, Spirit of Shankly, later said fans were left "fearing for their life" in a "maelstrom of chaos and alarm".
The Spirit of Shankly and the Liverpool Disabled Supporters Association hailed the decision but underscored that it did not go far enough.
A joint statement said the announcement "does not excuse UEFA, exempt them from criticism or lessen the need for them to implement all of the recommendations made by the Independent Inquiry".
The French authorities claimed an "industrial scale fraud" of fake tickets was the problem.
A French Senate enquiry in July found that poorly-executed security arrangements were the cause of the mayhem.
The independent report said that "UEFA, as event owner, bears primary responsibility for failures which almost led to disaster".
"We have taken into account a huge number of views expressed both publicly and privately and we believe we have devised a scheme that is comprehensive and fair," said UEFA general secretary Theodore Theodoridis.
"We recognise the negative experiences of those supporters on the day and with this scheme we will refund fans who had bought tickets and who were the most affected by the difficulties in accessing the stadium."
In a brief statement, the English club said: "This is a UEFA refund policy, not a Liverpool FC policy.
"The club's role, as a ticket agent for this match, will be to administer the refunds to qualifying supporters that bought match tickets via LFC, as directed by UEFA."
Images of the final tarnished France's reputation for holding major sports events ahead of the Rugby World Cup this year and the 2024 Olympic Games, both of which will host events at the Stade de France.
This year's Champions League final is due to be played in Istanbul, Turkey, on June 10.
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