The move doesn't necessarily come as a surprise. In the wake of the election, Obama had pledged to meet with the former Massachusetts governor and listen to his ideas.
The lunch, which will be closed to the press, marks the first time the two have met since the election, according to a White House announcement.
The bipartisan gesture comes at a time when Democrats and Republicans remain at loggerheads over how to avoid the "fiscal cliff" of scheduled tax increases and automatic spending cuts set to occur in January.