Major governing bodies are looking forward to a multimillion-pound windfall from the gambling industry after the government agreed to support demands for bookmakers to contribute a share of their profits to sport.

Tessa Jowell and Richard Caborn agreed at a meeting on Wednesday night to back the case of the five major sports - football, tennis, both codes of rugby and cricket - and Caborn will now contact bookmakers to try to negotiate a settlement.

The ministers' support marks a major victory for sports that have been pushing for a contribution from the bookmaking industry for some time, arguing that the growth in gambling revenue from sports other than racing entitles them to a share of profits. They also believe the growing betting market threatens the integrity of their events and will cost more to police.

The government has been unwilling to extend the levy system that applies in racing, but now accepts that sport has a persuasive "moral case" for a cut of the estimated £500m annual turnover in sports betting. The exact financial formula that will be used is yet to be determined, but the governing bodies would settle for a voluntary payment of between £5m and £10m annually in the short term. A system similar to the levy, where a percentage of profits is passed to sport, may also be considered. The sports for their part have agreed to spend any money they receive, which will be divided between the five governing bodies, on policing their events or on funding grass-roots programmes.