Three of the region's operators - First, Transdev and Arriva - have teamed up to launch Bus 18, a joint commitment to transform services for the better by 2018.
Under the new scheme, travellers who are unhappy with their journey can claim a free travel voucher from any of the three firms, and anyone trying to catch the last bus of the night can request a refund for a taxi journey if the service is more than 20 minutes late.
The changes came into force last Friday.
Punctuality will also be improved on five key routes, including the A65 between Leeds and Menston, while increased information about delays will be available.
The Bus 18 announcement was made in response to last year's Big Transport Consultation in Leeds, which revealed widespread concerns over punctuality, reliability, routes, timetables, value for money and ticketing.
The number of service changes has already been reduced, and new ticket options have been introduced.