The duo will both return for a second season in the junior single seater category having made their debuts with rival teams this year.
Despite missing the opening round at Symmons Plains, Fallon finished fifth in the championship standings with Dream Motorsport.
The 16-year-old from Victoria claimed a breakthrough race win at the Gold Coast final round last month along with the Rookie of the Year award.
Meanwhile, 15-year-old Everingham joins the South Australian operation after a year at Junior Racing Development.
The New South Wales driver was seventh in the standings with a fourth at Sandown his best result.
Team BRM boss Mark Rundle hopes the pair will continue their rise up the ranks next year.
“We are very excited to be able to welcome both Simon Fallon and Tyler Everingham to Team BRM. Both drivers proved this year that they are very talented,” Rundle said.
“We are looking forward to building on what they have learned this season and help them on the way to the next step in their careers.
“Simon really impressed me on the Gold Coast this year, he showed real poise for such a young driver fighting for a rookie championship.
“Tyler was very strong all year in his first attempt at F4, no doubt with a solid pre-season testing program he will be a star to watch come next year.
“2017 is going to be such a strong year for both second year drivers and rookies, we are pleased to have Simon and Tyler with us fighting for a championship.”