Italian-born Bellini will take up the role on 1 March. Since last July she has been vice-president, food for North America and managing director, food for the US at the FMCG giant.
She first joined Unilever in 1999 as a marketing manager in oral care, later holding marketing director and business director roles in Italy and central and eastern Europe. In 2012 she was appointed vice-president, brand development, North America.
Before joining Unilever, Bellini had a 12-year career in advertising, in both Italy and the UK.
Tesco chief executive Dave Lewis, who himself worked for Unilever for 27 years before joining Tesco in 2014, said: "I’m delighted that Alessandra is joining the team at Tesco. Her experience in building brands will be a valuable asset in the next stage of building a truly differentiated Tesco brand.
"She understands how to put the customer at the heart of business decisions, and has a great track record of building market-leading brands and teams. I am very much looking forward to having her on the team."
Bellini’s predecessor Terrell announced last summer that he would leave the supermarket after three years in order to "pursue a different direction". It was the latest in a string of changes at the top of the retailer, which began before Lewis joined.
He has since taken on non-exec director roles at Amara Living, Wilko and William Hill.