Abellio Northern, Arriva Rail North and Govia Northern are competing for the northern rail franchise while First Trans Pennine Express, Keolis Go-Ahead and Stagecoach Trans Pennine Express Trains are in the running for the transpennine franchise.
Both franchises are due to start in 2016.
Rail Minister Claire Perry said: “The north is undergoing a real rail renaissance, and we will be asking these companies to come up with innovative and ambitious proposals that will ensure a truly world-class rail network for the region.
“Building a railway that is fit for the 21st century is a vital part of our long term economic plan, connecting businesses and communities, generating jobs and boosting growth, and we need strong private sector partners to help us achieve this ambition.”
Wakefield Council leader Peter Box, chairman of the West Yorkshire Combined Authority, said: “We have long maintained that local rail users deserve to see levels of service comfort and capacity that match they quite rightly expect so it is good to see this level of interest in running these franchises.
“There is a continually growing demand for rail services in West Yorkshire and York and beyond so we look forward to seeing how the shortlisted companies intend to transform rail travel in line with the West Yorkshire Combined Authority’s objective of boosting jobs and growth.
A group of councils known as Rail North will be given a say in how the two franchises are run.
Manchester City Council leader Sir Richard Leese, for Rail North, said: “The companies on the shortlists demonstrate the interest there is in meeting Rail North’s desire to see the railway acting as an economic driver in the north of England.
“We look forward to working with the bidders to deliver strong franchises for passengers, which reflect the aims and objectives of our Long Term Rail Strategy and the predicted growth in patronage.”