The purchase adds to Rank's considerable holdings in the global packaging industry, a portfolio that the investment company has been building for the past year.
The company wants to expand its packaging presence into the lucrative US and European markets.
For processors SIG will make up part of a larger supplier, giving the company more leverage over setting prices for its packaging.
On the positive side, the move could also provide healthy competition in the market against Tetra Pak's dominance.
At SIG's general meeting today Rank will nominate its owner, Graeme Hart, along with Thomas Degnan, as its representatives on the board.
Robert Lombardini, a current SIG board member, Rolf-Dieter Rademacher, SIG's current chief executive, and lawyer Jakob Höhn will also be nominated to the new board.
Hart wants to merge SIG with other packaging holdings in Rank, his investment holding company.
In doing so he will set up a rival to Sweden-based Tetra Laval subsidiary Tetra Pak, which has an 80 per cent share of the carton packaging market.
SIG is currently the world's second-biggest maker of drink cartons after Tetra, with a 15 per cent share of the market.
Hart won control of SIG in a bidding battle earlier this year with European-based Ferd Holding and CVC Capital Partners, which in March ended their joint bid for the company.
Other items on the menu at SIG's general meeting include changes to voting rights and other technical measures to the public company's articles of association.
The changes are meant to consolidate's Hart's ownership of the company.
In April SIG's board reported that shareholders with 50 per cent of SIG shares had tendered them for sale to Rank, which already held a 34 per cent stake.
Rank's offer was CHF 435 in cash per SIG share.
The payment of the offer price is expected to be completed on 11 May.
SIG had sales of €1.2bn last year from products such as cartons for long life drinks and polyethylene terephthalate (PET) bottles.
Earlier this year Hart finalised a deal to acquire International Paper's drinks packaging business for €382.8m. The purchase allows Rank to sell products such as liquid paperboard packaging for dairy products and juice.
Hart has since sold the company's forestry unit to US-based Hancock Group for about NZ$1.5bn (€792m).
Last year he bought Carter Holt Harvey, the New Zealand timber and paper business.
Ferd and CVC's decision to drop out of the bidding war for SIG may have been influenced by the European Commission's decision on 22 December to open an investigation into whether their combination with the company would diminish competition in the market.
Both Elopak and SIG are suppliers of carton filling machines and carton material for non-carbonated liquid food products packaging.
Under EU rules the Commission had 90 working days, until 15 May, to take a final decision on whether the concentration would significantly impede competition.
The carton packaging market in the EU is characterised by a rather exceptional concentrated market structure with Tetra Pak dominating the market, while SIG and Elopak compete fir the rest of the business, the Commission noted.
Therefore the proposed transaction would combine the second and the third largest suppliers, while Tetra Pak would remain the largest competitor.