Paris and Los Angeles are set to stage the 2024 and 2028 Olympic Games - provided they can agree which should go first, as both want to host in 2024.
The International Olympic Committee has voted in favour of naming hosts for successive Games on 13 September with just Paris and Los Angeles bidding.
The IOC - which oversees the Olympic movement - wants the cities to reach an agreement on who hosts in 2028 by then.
If there is no agreement, a vote to select just the 2024 host will be held.
Budapest, Hamburg and Rome withdrew from the race for the 2024 event.
IOC president Thomas Bach told reporters after the meeting he hoped the agreement would be reached next month.
And LA organisers said they were "thrilled" with the decision, adding: "We look forward to working with the IOC and Paris in the weeks ahead to turn this golden opportunity into a golden future together."
In June, Los Angeles bid chair Casey Wasserman appeared to concede to Paris when he said: "We have never been only about 2024."
However, a spokesman later told BBC Sport: "LA is the ideal host city for 2024 and is not conceding anything in the race for the 2024 Games.
Paris has said it has to go first as the site it has earmarked for the Olympic Village will not be available for redevelopment after 2024.
Alex Capstick, BBC sports news correspondent:
It took a while and it was a little confusing but Thomas Bach eventually got what he wanted - unanimous backing for Paris and Los Angeles to become Olympic hosts.
It's dependent on all parties reaching agreement but with the mayors of the two cities, who are friends, holding hands while thanking the IOC members for their approval, it would be a major surprise if a deal isn't struck.
And there could be a quick decision. Discussions will begin in the next few days - it's in no-ones' interest for any uncertainty to linger longer than is necessary.
It's been dressed up as a win-win scenario. In truth one of them will be a bigger winner. Both cities started out bidding for 2024, now either Paris or Los Angeles will be asked to accept 2028 instead. It's still better than losing.
For the IOC it buys them time to revamp the bidding process, to encourage other potential contenders who have been scared off, especially in Western Europe. After years when competition was fierce to stage the prestigious event, there's been a declining number of cities that are interested.
Hamburg, Rome and Budapest pulled out of the current campaign, just two candidates competed for the right to host the 2022 Winter Games. The costs involved and a lack of public support were to blame.
Paris and Los Angeles have promised to do what is best for the Olympic movement. Greater collaboration, it seems, is the future of Olympic bidding.