Cardiff City is facing a winding-up order for an unpaid £2.7m tax bill.
The club has proposed the payments would start after five years, but will pay immediately if it achieves promotion to the Premier League.
Part of the deal stipulated that the club's construction partner will complete a public indoor sports facility known as the House of Sport on site, with work beginning within three months.
The club has requested a peppercorn rent on the House of Sport, and will provide offices in the complex for Cardiff council's sports development staff.
BBC sports reporter Rob Phillips said the agreement would raise finance for Cardiff City at an ideal time for the club.
"Highly-placed club sources have told me they're delighted and highly grateful to the council for what they've done," he said.
"Because this was in the offing, they didn't have to sell a player in the transfer window to raise money for the winding-up order."
Council leader Rodney Berman said: "Today's decision represents the best way forward for both the club and the Council.
"I also want to make it clear this is a beneficial arrangement and there is no question of the taxpayer bailing out the club.
"On the contrary this proposal will in time see money coming back to the council.
"Under this agreement the club's contractor partner aims to start work on the House of Sport within three months.
"This is going to be an important community facility, with indoor pitches and a multi-use sports hall. The proposal provides a much greater guarantee for securing the delivery of the House of Sport."
Source: BBC Sport
Source: BBC Sport