It is hoped the City Deal agreed by the UK and Scottish governments will lead to further investment from private companies and act as a "catalyst for economic growth and diversification" in the region.
The funds will support the new Oil and Gas Technology Centre in Aberdeen, the proposed expansion of Aberdeen Harbour, hubs for digital infrastructure, agricultural innovation and transport.
Details of the deal were first announced last year and the agreement was formally signed by Scotland's Economy Secretary Keith Brown and Scotland Office minister Lord Dunlop at a ceremony in Aberdeen on Monday.
Both the UK and Scottish governments are contributing £125 million to the scheme, which follows a similar deal for Glasgow signed in 2014.
Ministers believe the investment will create around 3,300 new jobs over the next decade and could also generate more tax revenues.
The Scottish Government is also investing a separate £254 million in the area to support transport and housing.
Mr Brown and Lord Dunlop were joined by Aberdeen City Council leader Jenny Laing and oil industry leader Sir Ian Wood, chairman of Opportunity North East, to sign the City Deal.
Mr Brown said: "The signing of the Aberdeen City Region Deal sends an unequivocal message that the Scottish Government is committed to boosting the north-east economy, and cementing Aberdeen's reputation as one of the world's leading cities for business and industry.
"This multimillion-pound deal will support Aberdeen's position as a global oil and gas hub, and it's fantastic to see the first tangible results of our investment through funding for the Oil and Gas Technology Centre which will help companies develop new products and processes that can reduce costs in the sector."
Lord Dunlop said: "The £250 million Aberdeen City Region Deal will make a huge difference to the region's economy, helping to boost jobs and prosperity. It is great news that we are signing the deal today, meaning we can get on with driving growth in the economy of north-east Scotland.
"A key part of the deal is to support innovation and diversification in the oil and gas industry, which is why the technology centre is so crucial. I am very pleased this week that the UK and Scottish governments have been able to release the first £4 million of funding, which will enable the Oil and Gas Technology Centre to begin its important work."
Sir Ian described the agreement as a " strong vote of confidence from Westminster and Holyrood in the dynamism, resilience, innovation and growth potential of our key industries".
He added: " Transitioning Aberdeen from a centre of operations in offshore oil and gas to a globally-recognised leader in mature basin technology via the Oil and Gas Technology Centre will anchor at least some of our supply chain post the North Sea."