The move will substantially boost Premier's portfolio of well-known British brands - the top ten of which are expected to bring in total sales of around £1.1bn (€1.6bn) for the company.
Today's deal will put Premier back on track in its efforts to become a greater force in the UK snacking sector after it was thwarted in a bid for United Biscuits' cookie divisions earlier this year.
Premier Foods, who own the Branston Pickle and Ambrosia dessert brands, said it would be incorporating RHM's culinary brands, cake and customer partnerships divisions into its grocery sector while the company's bread operations would continue as a stand-alone business due to the distribution model and milling operations involved.
Premier's portfolio will now include bakery brands Hovis and Mr Kipling - both of which have seen an upturn in sales stemming from a 'healthy' revamp earlier in the year.
Premier's chief executive Robert Schofield said: "This acquisition brings Premier more great British brands with leading category positions which fit naturally in our portfolio. As we've done before, we intend to drive growth through innovation and investment whilst maintaining a tight control on costs."
For the year ending April 2006, RHM's bread bakeries division recorded sales of £786m (€1,168.5m) and underlying operating profit of £81.4m (€121m).
The company's cake sector is also a strong performer with sales of £241m (€181m) and profit of £13.7m (€10.3m) in the same period.
The merger of Premier Foods with RHM will create the largest UK food processor and is forecast to have annual sales of £2.6bn (€3.8bn).
RHM Chairman Jan du Plessis said: "The Board of RHM has long appreciated the commercial and financial logic of a combination with Premier to create the leading UK-focused food manufacturer."