This is one of the phrases that, while having been long attributed to Shakespeare, was in fact used earlier by others and has now been demoted to ‘popularised by’ rather than ‘coined by’ the bard. There is a definition of the expression in Thomas Cooper’s glossary Thesaurus Linguae Romanae Britannicae, 1578:

To eate out of house and home: to waste and consume his substance, money etc.