The Square Chapel in Halifax has been awarded more than £3.9m for its Cornerstone project to link the building to the nearby Piece Hall.
Ben Rothera, from the chapel, said: "We really want to transform this part of Halifax into a cultural quarter."
The Art House will receive more than £1.5m to develop an old library building on Drury Lane, Wakefield.
Halifax's Square Chapel was built in 1772, one of the few square churches built, the derelict building was bought in 1988 to convert into an arts centre.
Along with the new extension the building will get a new auditorium, a cinema and live screening facilities in a development costing almost £6m.
Mr Rothera, the Square Chapel's marketing manager, said the award was the biggest day in the history of the chapel as an arts venue.
The building will eventually link to the Piece Hall, which is also to undergo a £19m refurbishment.
In Wakefield the money will see a second phase of development for the Art House, which opened in 2008 with 14 accessible studios.
The grant will create a further 34 accessible studios by knocking through to connect with the former library next door.
Anne Cunningham, chief executive of the Art House, said: "It's not easy to sustain working as an artist but a studio is an important place for them."
The organisation also runs business skills courses for its artists.
Two arts organisations in West Yorkshire are to receive £5.5m in lottery funding from the Arts Council.