The deal is pending a physical, according to a person familiar with the negotiations who spoke on condition of anonymity because the contract had not been finalized.
After spending the past three seasons with the Los Angeles Angels, Oliver is set for his third stint in Texas. The 39-year-old left-hander began his career with the Rangers, pitching for them from 1993-98. He was back with Texas from 2000-01.
Oliver was 5-1 with a 2.71 ERA in 63 games last season. His deal would include a $3 million salary next year and a $3.25 million option for 2011 with a $500,000 buyout. The second year of the contract would become guaranteed, however, if Oliver makes 60 appearances next season.