The event, which will see athletes competing for places at next month's European Indoors in Belgrade, takes place on 11-12 February at the English Institute of Sport in Sheffield.
Olympic heptathlete Katarina Johnson-Thompson goes in the 60m hurdles and the long jump, with Andrew Pozzi - who set the fastest time of 2017 so far in Germany on Saturday - competing in the men's 60m hurdles.
Pozzi's 7.44 seconds in Karlsruhe was the third fastest time in British history.
Johnson-Thompson will face Olympic finalist and European silver medallist Jazmin Sawyers and world indoor bronze medallist Lorraine Ugen in the long jump.
British Athletics' major events director Terry Colton said: "The support of the BBC will enable us to showcase the event to more people than ever.
"We're really pleased the British Athletics Indoor Team Trials will reach anybody who wasn't able to get a ticket or isn't able to make it to Sheffield this weekend."
The BBC will have live commentary from Kris Temple and Adrian Chrismas, and analysis from world and European medallist Jenny Meadows.
The British Athletics Indoor Team Trials will be broadcast live on the BBC Sport website this weekend.