The company did not disclose the details of the transaction.
"This acquisition marks our entry into the European market and plays an important role in realising our ambition of becoming one of its key players," Hero Cycles Chairman and MD Pankaj Munjal said in a statement.
He further said: "We are hopeful that our respective teams will have the opportunity to work together and use our respective strengths to manufacture and distribute world-class products to customers in the UK and continental Europe".
Avocet offers a range of products including hybrid, children's bikes, e-bikes, mountain bikes, BMX and roadster. Its leading brands include Viking, Coyote, Rooster, Ryedale, Lectro, Concept and Riddick.
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Commenting on the development, Avocet Chairman Steven Walsh said: "I am looking forward to working with the Hero team to develop the UK & European markets together."
Munjal had recently outlined the Ludhiana-based cycle manufacturer's plans to focus attention towards capturing significant market share in higher-value cycle markets such as the UK and Germany.