RHM's board has approved the deal that will bring together names such as Hovis bread, Mr Kipling cakes and Oxo gravy, although the purchase still needs to be approved by shareholders of both companies.
The merged company will have annual sales of £2.6bn, with 93% of those revenues coming from the UK.
Premier chairman David Kappler said. "This acquisition provides a unique opportunity to combine two of the UK's leading food companies."
Premier, owner of brands such as Branston sauces and Ambrosia Creamed Rice, will pay a mixture of cash and new shares in a deal that values RHM stock 30% higher than its Friday close.
Premier said it would pay one new share and 83.2p in cash for each RHM share, working out at about 352.45p for each RHM share.
News of the deal sent shares in both companies up sharply. RHM shares soared 35% in early trading while Premier's shares rose 8%.
RHM Foodservice launches healthy school food award >>By Daniel Thomas
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