''We have a great opportunity to hit this ball out of the ballpark,'' he said.

Fans were boisterous that the team -- which will change its name to the Miami Marlins -- would finally have a home of its own . . . and a promise to stay in Miami for 35 years.

''I didn't sleep last night, hoping this is the last time I'm in front of the mike to ask for a stadium,'' said Gilberto Lauzardo, a Hialeah fan wearing a bright orange Marlins shirt.

Thursday's votes came over the objections of some residents who said hundreds of millions of dollars in taxpayer money should not finance a sports complex without the issue going to a public referendum.

Chief among them: auto magnate Norman Braman, who has challenged the deal in court.

''Mr. Braman would drop this lawsuit in a heartbeat if you allow it to be voted in a public referendum,'' said Harley Tropin, one of Braman's lawyers.

Tomás Regalado was the lone no vote on the City Commission, saying he objected to the stadium being tied into a larger $2.9 billion megaplan.

The 'no' votes at county hall came from Carlos Gimenez, Sally Heyman, and Javier Souto. Commissioner Katy Sorenson was home recuperating from surgery.

''My heart would love to vote for this but my head just can't,'' said Gimenez, who was worried about the impact of Braman's lawsuit, profit-sharing with the team and other terms of the deal. ``We're rushing into something where we don't have all the facts.''

But supporters carried the day.

''Just like museums, parks and beaches, professional sports are an important part of our community's fabric,'' said County Mayor Carlos Alvarez. ``A stadium will not only contribute to our economy, but to our quality of life.''

The Marlins hope to be in their new home by Opening Day in 2011.

Though city, county and team representatives still must negotiate the fine points of some issues -- such as stadium maintenance and construction -- Thursday's written agreement represents a huge milestone in the ball club's quest for a modern, baseball-specific facility.

There were a few tense hours, however, as the county's police and firefighter unions demanded that their workers -- rather than the city of Miami's departments -- get the exclusive right to work the 30-odd off-duty jobs within the ballpark.

The county departments are still smarting that the city holds almost all those jobs at two other county-owned facilities: AmericanAirlines Arena and the Adrienne Arsht Center for the Performing Arts.

''Your men and women -- who have been slaughtered recently -- have been cut out,'' said John Rivera, president of the Police Benevolent Association.

But if the county had amended the contract to clarify the jurisdiction, the City Commission's early vote would have been nullified; it would have needed to hold a new vote.

Moreover, city police would not have lightly given up access to those jobs.

''I think the city of Miami should work it -- it's going to be called the Miami Marlins,'' said Armando Aguilar, president of Miami's Fraternal Order of Police.

Rather than suffer a delay and resting the entire deal on that turf fight, the county decided to spend the next month in side negotiations with the city.

''We should all be ashamed if we can't resolve that issue in 30 days,'' County Manager George Burgess said.

After that was resolved, concerns about small-business set-asides in the construction nearly forced a similar delay. Those details, too, will be resolved in more detailed agreements this summer.

With the two governments' approvals Thursday, preconstruction design and site preparation work will likely begin in the coming months. Ground should be broken in November.

''It's been quite a road to this day,'' Marlins president David Samson told city commissioners. ``And it is true sometimes, what they say in the movies, that dreams can come true for families and for fans.''