Both unions have more than 4,000 members each at Sars.
According to the agreement, employees will also get a salary increase of projected CPI (inflation) plus 2%, effective from April 1 2020, and April 1 2021.
The long-service award amount will increase annually with the same percentage as a salary increase. Workers will also be entitled to eight days' pre-natal and vaccination leave and five days' family responsibility leave in a two-year leave cycle.
"We trust that Nehawu will come back and accept the offer that has been put on the table," Musekwa said.
Newly appointed Sars commissioner Edward Kieswetter, who starts work on May 1, said in an interview with the SABC on Monday that he was in touch with acting commissioner Mark Kingon about the strike.
"No one wins under a strike. Neither the organisation nor the staff wins under the strike. But when the staff eventually reach the point where they withhold their labour, it is endemic of a culture that needs to be addressed," said Kieswetter.