The two UK companies both offer pharmaceutical packaging services such as injection blow moulding, extrusion blow moulding and secondary decorating.
They also share some of the same customers.
"The two businesses are extremely complementary to each other and will have a strong market position in healthcare packaging", Cope Allman managing director John Sidnell said of the deal.
Cope Allman plans to keep both its existing plant in Portsmouth, along with Jaycare's newly-acquired site in North Tyneside, fully operational and the merged businesses will now trade under the name of Cope Allman Jaycare.
It is anticipated that together, the new entity will reap in more than double the annual sales that Cope Allman has been generating on its own (£12m).
The deal was supported by the One NorthEast development agency, which promotes business in the North East of England, where Jaycare is located.
Failure to find a buyer would have led to the closure of the site and the loss of around 200 jobs in the region.
Although Sidnell has admitted that following the acquisition "some rationalisation will be inevitable" , he did say he expects that "the majority of jobs will be secured".
Cope Allman is currently undertaking a business review of its new purchase.
24 assembly workers at the Jaycare site were already made redundant in December after the firm suffered the loss of a "major" contract that it had relied upon for over 10 years.
At the time it was also announced that further job cuts were being mulled over, although it appears this contract loss was the straw that finally broke the company's back, as it was subsequently placed into administration weeks later on 16 January after going bust.
Since then its fate has been hanging in the balance, as its joint administrators, Mark Firmin and David Crawshaw, of KPMG's Restructuring practice in Newcastle, searched for a buyer.
It is hoped that the new owners will finally bring some stability for the company, which has witnessed a several changes in ownership over the last few years.
It underwent a management buyout in 2000, and in 2004 when profits started diving, it was subsequently purchased by London-based venture capital firm Phoenix Equity Partners for £47m.
At the time Phoenix said it was planning to offer an abundance of funding to enable the growth of the business and its profits, although as the company continued to bleed cash, Phoenix bowed out in 2006, and Jaycare was refinanced and restructured, with the company's management once again becoming the majority shareholder, backed by £4m from Allied Irish Bank and HBOS, in a failed bid to keep the business afloat.