The Boston City Council voted 11-2 today to approve a redistricting map that at the last moment won broad support after 16 months of wrangling fraught with electoral politics and racial undertones.

The map that passed was crafted by Councilor Tito Jackson, who amended a proposal from other councilors. It came as a rebuke to Councilor Bill Linehan, the chairman of the Redistricting Committee, who had lobbied against Jackson’s amendments.

“It moves the city of Boston forward,” Jackson said, describing the plan as “lasting and indelible lines” for “a city that is a majority people of color and a city that cares about everybody.”

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The vote sent the measure to Mayor Thomas M. Menino, who will sign it after vetoing two earlier plans, according to his spokeswoman, Dot Joyce. The vote in the City Council was “reflective of the city,” Menino said, according to Joyce. Menino remained hospitalized today with a respiratory virus and a blood clot in his leg.

Today represented a hard deadline for councilors because a new map for the nine City Council districts had to be adopted and signed by the mayor a year before the next municipal election in 2013. The council had narrowly approved two previous maps, but Menino rejected the plans, saying both concentrated too many black, Hispanic, and other voters of color in too few districts.

On Wednesday, Jackson and Linehan were animated as they advocated their plans, which only differed by five precincts. Both men spoke on the floor of the council chamber with a rare bluntness about race and electoral politics. At one point, Linehan, who is white, noted that Jackson, who is black, won his district by 90 percent and that “taking on a few white people isn’t going to kill Councilor Jackson.”

After the vote, Jackson and Linehan shook hands and halfway embraced with one-armed hugs. After the meeting, Linehan made it clear that he held no ill will toward Jackson, even if he voted against the plan that passed.

“He was doing what he thinks is best for his constituency. I’m doing the same thing,” Linehan said. “So I didn’t win this time. But I think the city of Boston has a new plan that everybody can work with.”

Some of the most significant changes will be in District 5, which includes Hyde Park and part of Mattapan. In the new map, it will gain several more Mattapan precincts, making it significantly more diverse. More than 70 percent of residents will be ethnic minorities and almost 50 percent of the voting-age population will be black.

“What I’m really proud of is that District 5 has seen the greatest and most historic change,” said Councilor Rob Consalvo, who is white and has represented the district for a decade. “It really creates that fourth strong district of color – black and African-American — that was asked for by so many advocates across the city.”

At the same time, the new map removed Mattapan precincts from District 4, which is a point of contention for Councilor Charles C. Yancey, who joined Linehan in voting against the plan. Yancey had pushed his own redistricting proposal and several residents from his district attended the hearing to show their support. Yancey failed to win the support of any his 12 colleagues on the City Council.

The map will also have a significant impact on District 3, which encompasses much of Dorchester. The district will lose precincts in Lower Mills and along Dorchester Avenue.