The Heritage Lottery Fund money will go towards an extension and redevelopment, promising to bring the landmark's Grade I-listed Fratry building "back to life".
The Dean of Carlisle, the Very Rev Mark Boyling, said: "We're delighted that we have received this support from the Heritage Lottery Fund."
Work is due to start next year on providing a wheelchair-accessible teaching and learning area at the Fratry building, which will also boast new catering and hospitality facilities.
The building should be ready by summer 2019.
Dean Mark Boyling added: "The Cathedral is open and active every day of the year and we need the right facilities if we are to meet the needs of the many people from the city and far afield who come to this must-see location with a message.
"It is good to know that we will be able to reach more people in new ways."
Leaders say the new Fratry building will offer a new space for exploring the "stories" and "treasures" of the cathedral, which is almost 900 years old.
Nathan Lee, Head of Heritage Lottery Fund North West said: "This is an important project which the Heritage Lottery Fund is delighted to be able to support.
"Lottery players' money will be put to excellent use by the Cathedral, which will as a result be able to offer better facilities and opportunities to engage with heritage, for both local people and visitors to this wonderful city."