Greybull Capital, a UK-based investment firm, is to plough up to £400m into the plant - but workers had to accept a pay cut and smaller pension contributions.
In an earlier ballot, Community, Unite and GMB members accepted temporary changes to their terms and conditions.
Officials said it was a positive step in "securing a sustainable future" for the plant.
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Unite's National Officer, Harish Patel, said: "This will have been a difficult decision to take for many, but by agreeing to make these short-term sacrifices, members have secured a future for steelmaking in Scunthorpe and the long product division's other sites.
"Government ministers need to make sure that the sacrifices are not being made in vain by taking decisive action to support the steel industry and allowing steelworkers to compete on a level playing field with their global competitors."
Steve McCool, from the union Community, echoed calls for Government action.
"He said: "The steel made at Scunthorpe and across the north of England is some of the best in the world and is absolutely vital to the infrastructure and construction industries."
"When Britain builds, we must always build using British steel," he said.
The Government is yet to respond to a request to comment on what the union leaders have said.
Ahead of the vote, steelworker Charlotte Upton said the proposed deal meant "job security for me so I can stay where my family is, near my home".
"It means I can continue to be a steelworker, I love my job."
The proposed temporary changes to terms and conditions include a one year, 3% reduction in pay, and a one year, 3% reduction (from 6%) in both employer's and employee's pension contributions.
The Tata signs will be also removed and replaced with ones saying British Steel.
The Scunthorpe steelworks is part of Tata Steel's long products division, which was put up for sale in 2014.
Workers have voted to accept a deal which will safeguard about 4,400 jobs at Tata's steelworks at Scunthorpe.