The company's managing director Mike Hedges told the Press Association that the up-market crisp maker is poised for a growth spurt following the £300m deal.
"We have no business in North America and Amplify has no business over here. They're going to take the Tyrrells brand and roll it out in North America and we'll take their SkinnyPop brand, and others, and do the same in the UK.
"We'll have to take on more staff to do that and I'd say that, over the next three years, we'll recruit hundreds globally."
Tyrrells currently employs around 500 people globally and the firm, whose stable of products include potato, vegetable and crinkle cut crisps and premium popcorn, raked in £84m in revenues over the past 12 months.
Mr Hedges also brushed aside any fears that Britain's decision to quit the European Union would take a bite out of sales.
He said: "In 2008, during the last recession, none of the premium crisp brands suffered and I don't think they will this time either - if there is a downturn."
Click below to sign up for daily business updates
Our BQ Bulletin emails will land in your inbox at 7.30am, Monday to Friday, with a mix of the latest local business news, national news, and features to inspire you. Sign up here!
Click here to read our privacy statement