It is named for Hon Vaiben Louis Solomon, a Premier of South Australia, a delegate to the second Constitutional convention and member of the first Australian Parliament.

Although the Darwin/Palmerston area had historically been a stronghold for the Country Liberal Party at the territorial level, recent gains by Labor made it much more competitive by the time the seat was created.

A MediaReach seat-level opinion poll in Solomon of 513 voters conducted 22−23 June during the 2016 election campaign unexpectedly found Labor heavily leading the Liberals 61–39 on the two-party vote from a large 12.4 percent swing.

[2] Griggs and the CLP lost Solomon to Labor's Luke Gosling, at the 2016 election held on 2 July, with Gosling becoming the first Labor candidate to win the primary vote and defeating Griggs on a 56–44 two-party vote from a record 7.4 percent swing—in both cases, the strongest result in the seat's history.

This was later seen as a forerunner to the CLP's disastrous performance at the NT general election held later that year, where the party won just 2 seats out of 25, including only one in the Darwin area.