She replaces Kari Daniels in the role, who has decided to step away from the retailer.
Adams will report to group chief executive Ken Murphy in a new role on the Tesco Executive Committee, Tesco said in a statement.
"Natasha has made an outstanding contribution in her role as chief people officer, and her appointment to the new role of Chief Executive Officer, Tesco ROI, recognises the breadth of that contribution," Murphy said of the new appointment.
"I have no doubt she will bring the same blend of strategic thinking and people-centricity, as she leads our Irish business into an exciting future.”
Adams has served in a number of roles since joining Tesco in 1998, including business support director for the UK, executive owner at Tesco Business Services, and customer services director.
The Kerry native took on the role of chief people officer in June 2018.
Departure Of Kari Daniels
On Kari Daniels' time at Tesco, during which she held various senior commercial and marketing roles, Murphy added, "I’d like to thank Kari for her significant contribution to our business during her time in Ireland and throughout her 20 years at Tesco."
Tesco Ireland recently announced plans to acquire ten Joyce’s Supermarkets in Galway, pending approval by the Competition and Consumer Protection Commission (CCPC). The retailer currently holds a 22.2% share of the Irish grocery market, according to Kantar.