Arriva Rail was awarded the Northern franchise covering the majority of local services while FirstGroup will run Transpennine Express services connecting Yorkshire to the North-West and Newcastle.
Ministers said the deals would see £1.2 billion invested in services including 500 new carriages, the phasing out of Pacer trains - branded “buses on rails” by commuters - and the introduction of 125 mph services on some transpennine routes.
The Government said benefits of the new franchises would include extra capacity on trains in and out of Leeds and Sheffield at peak times and improved services for Bradford and Hull.
The deals include £1.4 million of improvements to Hull station ahead of City of Culture 2017.
Transport Secretary Patrick McLoughlin said: “We promised passengers across Yorkshire and the Humber a world class rail service that would make the Northern Powerhouse a reality – and I’m delighted that we have found two operators that will deliver exactly that.
“As a one nation government we are committed to closing the economic gap between north and south.”
Arriva is promising to increase capacity on the morning rush hour into Leeds and Sheffield by close to half and introduce a range of new services between Yorkshire’s towns and cities.
Chris Burchell, managing director of Arriva’s UK Trains division, said: “We are proud to be given the opportunity to transform rail travel for passengers in the north of England and to work closely with our partners to connect towns, cities and communities like never before.
“We will be investing more than £1billion to deliver a step-change in quality for customers and dramatically improving services, stations, information and ticketing. Our aim is to be the communities’ local railway and to leave a positive lasting legacy for the north of England.”
First will bring in 220 new carriages on the Transpennine services including new longer trains between Scarborough, Leeds, Manchester and Liverpool.
There will also be extra services between Leeds and Hull and on the Newcastle, York, Leeds, Manchester route.
Tim O’Toole, chief executive of FirstGroup, said: “Our new TransPennine Express franchise will deliver faster and more frequent intercity train services between the north’s major towns and cities and we are excited to help the government achieve its vision for a Northern Powerhouse. Our plans include investment in new and refurbished trains on every part of the network, with millions more seats available, free Wi-Fi and simpler smart and mobile ticketing, allowing us to build on the success we have had over the past 11 years, in which we have more than doubled passenger journeys on the network.
“We will work with local authorities, customers and community groups to give them a real stake in the future of their intercity rail travel. The new TransPennine Express will connect the north and keep people moving and communities prospering across the region.”
Arriva previously held the northern franchise from 1997 to 2004. In 2001 it was fined £2 million by the Strategic Rail Authority for poor performance, after coming in for heavy criticism from passengers when it announced it would cut more than 1,000 services a week because of a driver shortage.
In 2000, Arriva paid more than £9 million to the authority after failing to meet performance targets.
In 2003 an all-party MPs’ report criticised the company for the time it took to take action on staffing problems, which it said had led to “appalling passenger services, with trains delayed or cancelled”.