The new centre, which is being designed by local practice Brock Carmichael Architects, will house a presentation theatre, archive gallery, restaurant and dining patio.
The grant from the Merseyside Objective One will go towards a proposed £2.5 million extension needed to handle the increasing visitor numbers to Britain's largest cathedral.
According to estimates, the number of people passing through the doors of the Grade I-listed building is expected to rise from 34,000 to more than 470,000 by 2010.
Richard Nutter, the director of the Objective One programme, said: 'The Anglican cathedral stands tall in the history of Liverpool as well as on its skyline.
'These new facilities will explain both the history of the building and the way it continues to play a very important part in the life of the local community.'
He added: 'It is such a beautiful building that every year hundreds of thousands of people visit it, whether they are religious or not.
'[The centre] will ensure that one of the city's most treasured landmarks can be enjoyed by the greatest number of people.'