The City Council made the handshake deal official early Thursday morning, passing a $75 billion budget and taking a second time to tout what was in it and effusively thank each other and Council Speaker Melissa Mark-Viverito for getting it done.

“We are really touching the lives and making an impact on the lives of thousands and millions of New Yorkers,” Ms. Mark-Viverito said at the council’s meeting that kicked off after midnight Thursday morning.

The budget was adopted at 1:18 a.m., with 50 in favor and just one abstention — Councilman Ruben Wills, who is currently under indictment on fraud charges.

In addition to money for resolving labor contracts and the mayor’s key initiatives, it also includes priorities won by the City Council — overhauls at Rikers Island, free lunch for middle school students, and security at the city’s Housing Authority.

But it does not include everything the council asked for – there’s no funding for 1,000 new cops, though there is a plan to take 200 off desk duty and put them on the streets, and the free lunch program is for just middle school students rather than all students.

There was little talk of those shortfalls. In something of a replay of the handshake announcement, just without the mayor, member after member praised the speaker, Councilwoman and Finance Chair Julissa Ferreras, the budget and one another — though they did it quickly in light of the late hour.

Council members found plenty of reasons to thank Ms. Mark-Viverito — for her leadership, for listening, for making the process more transparent and friendly than it had been in the past. They lauded the budget itself as progressive and transparent.

Minority Leader Vincent Ignizio and his fellow Republican Councilman Steven Matteo were among the only members to offer criticism of the budget deal.

“I still believe there was room in the budget for additional police officers, and we will continue that fight,” Mr. Matteo said.

Mr. Ignizio echoed that concern and said he thought the budget “spent too much.” But he also praised the council and the speaker for the budget process, and for diluting her own power in how the council hands out discretionary funds.

Mr. Wills, meanwhile, said he abstained due to unanswered questions he had on the budget.

The document includes some $50 million in discretionary funding, or member items, that council members will dole out to programs in their districts. While Mr. de Blasio had repeatedly said he would look to do away with member items, after the speaker rolled out reforms to them Mr. de Blasio said they reached a “détente.”

This year, the member items were apportioned using a new formula – with a base of $400,000 per member, and additional money awarded for districts based on rates of poverty.

In the past, member items were handed out at the speaker’s discretion – leading some to say they could breed corruption, and others to complain that Speaker Christine Quinn used them to reward or punish members.

Ms. Mark-Viverito said the change “has ensured that no district is losing out because of politics.”

The council held its vote on the budget in the middle of the night, in part due to those member items. They cannot vote on the budget until 24 hours after the “schedule C” – which outlines the member items – is released. That document was made public at about 9:20 p.m. Tuesday.

While the Council could have waited for the next day — the budget is due by month’s end and a Thursday meeting was already scheduled– it voted overnight, as it often has, while many New Yorkers were asleep. The vote was tallied after 1 a.m., not long before the body is slated to meet yet again, Thursday afternoon, to vote on municipal identification cards.

Ms. Mark-Viverito tweeted the late hour was not how she wanted to pass her first budget, and several council members joked about the late hour.

“Permission to explain my vote? No, I’m just kidding. Aye on all,” the first voter, Councilwoman Maria Del Carmen Arroyo, said.