Lewis, 48, will join the Sri Lanka team after the Test series against New Zealand concludes, on December 30, and has a contract that will take him through to the end of the 2019 World Cup.
A highly-rated coach in England, Lewis oversaw the latter stages of Durham's run to the County Championship crown in 2013, and coached the team to the one-day title the following year. Under him, Durham were also Natwest Blast runners-up in 2016.
"With his expertise and experience, I believe, Lewis will be able to bring in the required impetus to our batting, which needs stability," SLC CEO Ashley de Silva said.
Lewis played 205 first-class matches from 1990 to 2006 and amassed 10,821 runs at an average of 31.92 with 16 centuries.
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Samaraweera is likely to remain in Sri Lanka Cricket's employ, and will probably take up a role in the high performance centre in Colombo, where he will work with developing and age-group players.
Lewis' appointment is one of several recent changes to the Sri Lanka set-up, following poor home series against England. In addition to a new batting coach, Sri Lanka have a new set of selectors led by Ashantha de Mel, as well as a new fielding coach in Steve Rixon, who is expected to join the team ahead of the second Test in New Zealand, which begins on December 26, in Christchurch.