The site produces composite structures and complex machine parts for aircraft such as the Black Hawk helicopter.
GKN was valued at 5.7 billion pounds at the close of Thursday.
Investors have been calling for GKN to split its businesses as management persistently failed to meet targets to improve profit and cash flow despite growing sales.
The maker of components used in the Black Hawk helicopter and by automakers such as Volkswagen and Ford cut its profit outlook in October, hurt by a writedown at its USA aerospace division.
Commenting about GKN's intention to separate the businesses, Melrose said it believes that shareholder value would be maximised by it significantly improving the businesses prior to any separation.
Shares in GKN were up 26% at 420.00 pence on the news, valuing the company at GBP7.26 billion, and having hit an all-time high of 425.00p earlier in Friday's session.
The bid was rejected, but GKN promptly admitted that it would now start the process of a demerger.
On the appointment of Stevens as new chief executive, the firm's chairman Mike Turner said she "has the track record to transform GKN", pointing to her "successful turnaround" of The Ford Motor Company's Mexico, Canada and South America businesses and senior roles at Carpenter Technology and Lockheed Martin.
It later warned the writedown would be bigger than expected and announced the departure of CEO-designate Kevin Cummings, the head of the aerospace division who had been set to take over the top job this month.
"Her operational and strategic skills are ideally suited to GKN and the Board is very impressed with the contribution she has made so far in setting out plans for a significant improvement in the Group's performance", he added.
Regarding the rejection of the Melrose offer, GKN said the offer is entirely opportunistic and that the terms fundamentally undervalue the company and its prospects. GKN shareholders would have held around 57 per cent of the combined group.
A downturn in GKN's performance had reignited speculation it might separate its two divisions and restructure the business, which employs 58,000 people across 30 countries.
"GKN is a world leader with the potential to perform even better", she said.
Engineering company GKN is long established in the United Kingdom and internationally with aerospace and automotive operations.
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