Hill, 19, will be one of 10 overseas competitors among the 16 drivers confirmed for the series from January to March.
He will be accompanied by his father, 1996 F1 champion Damon Hill.
His grandfather, Graham Hill, was a two-time F1 champion and also won the New Zealand Grand Prix at Pukekohe in 1965 and 1966.
Josh Hill said he wanted to race in a series similar to the Formula Renault and the TRS fitted the bill.
As for following in his father's footsteps, he said he didn't feel the pressure that people thought he should.
"Once I'm up at the race track, that's not even registering in my mind," he said.
"It's all about what's going on at the track. To me, my dad's just my dad."
Among the other foreign drivers are Russians Danill Kvyat, 16, Ivan Lukashevich, 19, and Sergey Sirotkin, 15. Englishman Alex Lynn, 17, is fresh from winning British 2.0 Formula Renault Winter Championship; Kotaro Sakurai, 16, will be the first Japanese in the series; while Mario Farnbacher, 18, will fly the flag for Germany.
Two of the three Australians in the field won British racing titles this year. Scott Pye, 20, dominated the Formula Ford Championship, while Jordan Skinner, 19, won the 1600cc Formula Ford competition.
The New Zealand contingent includes 16-year-old defending champion Mitch Evans of Auckland, while veteran Kenny Smith intends to be on the grid for at least the New Zealand Grand Prix at Manfeild in February.