Chancellor George Osborne confirmed an agreement on a ‘new City Deal' with the West Yorkshire combined authority in his Budget speech today.
The combined authority struck the growth deal despite resisting pressure from the Treasury to accept an elected mayor, as in Greater Manchester.
A spokesman for the West Yorkshire combined authority said the deal allowed for ‘negotiations on further devolution of powers and investment with any future governance changes being subject to consultation by the combined authority'.
Combined authority leaders admitted the deal ‘fell short' of the city region's economic ambitions but called it a ‘starting point'.
Chair of the authority, Cllr Peter Box, said: ‘The deal is disappointing and doesn't match the scale of our ambition.
‘It undermines the Government's claim to want a strong Northern Powerhouse.
‘If we are to turn that into a reality we need real devolution, including fiscal devolution, to enable us to bring about a step change in the city region's economy.'
Leeds City Council leader, Cllr Keith Wakefield, added the deal was ‘no compensation' for the £470m of cuts that the region's councils have had to deliver.
He added: ‘We shall continue to lobby and campaign for the greater powers and resources, including fiscal powers, that we need to achieve our ambitions and start the process of tackling the north-south economic divide.'
The deal is in marked contrast to the one reached with Greater Manchester, which has been granted devolution of power over numerous areas including health budgets.
Mr Osborne also pledged to give ‘more power' to Wales, with work underway on a City Deal for Cardiff.
And he said efforts would continue on the ‘historic' devolution deal for Scotland, with negotiations on City Deals for Aberdeen and Inverness expected.
Aberdeen City Council leader, Cllr Jenny Laing, said: ‘I am delighted for Aberdeen and the whole of north-east Scotland that the Chancellor has today indicated he is willing to enter formal discussions on a City Region deal with our officials.
‘The proposals we have outlined will ensure the prosperity of our city and north-east Scotland for decades to come by anchoring an economy of global significance for the benefit of the UK as a whole.'
He said: ‘London is the global capital of the world and we want it to grow stronger still.
‘We don't pull the rest of the country up by pulling London down.
‘Instead we will build on London's success by building the Northern Powerhouse.'
Mr Osborne claimed the North grew faster than the South over the last year and that the Government was closing the gap between the two regions.