Wigton-based Innovia said it plans to build a £20m factory to produce material for the new £5 and £10 notes. The Bank of England says polymer notes will be in circulation in 2016 - replacing cotton paper notes, which have been used for more than 100 years.
Innovia makes plastic packaging and already employs about 800 people in Wigton.
A £5 note featuring Sir Winston Churchill is due to be the first plastic banknote. They will be made from a thin, transparent and flexible film made of polypropylene.
This will be coated with an ink layer enabling it to carry the printed design features of a banknote. It also allows the inclusion of windows or clear portions in the design, used to enhance protection against counterfeits.
The Bank of England has said that the notes will last for two-and-a-half times longer than paper banknotes. They would survive a spin in a washing machine but would still melt under extreme heat such as an iron.
More than 20 other countries around the world have already adopted polymer banknotes.
David Beeby, chief executive officer of Innovia said the firm was very proud to have been selected as the preferred supplier and said the decision "recognised Innovia's expertise in this field."