Founded in 2014, the company has developed a technology that could cure blindness.
Nightstar is the latest in a number of UK-based healthcare companies looking to US markets for IPOs. Investors in the US are said to have a better understanding of biotech, which leads them to value early-stage companies at higher amounts.
Nightstar is set to float at an estimated valuation of $250m.
The firm has raised funds through three rounds of investment, the most recent of which raised $45m in June.
The London Stock Exchange has not lost out on all recent floats in the sector, however. Last month, biotech company Destiny Pharma said it was plotting a London float.