Bell, a 58-year-old motorcycle dealer, was competing with his son Carl who was his passenger and was not injured in the crash at Ballaspur, ACU Events said in a statement.
Soar, 32, was an experienced competitor on the Mountain Course. He died in an accident at Keppel Gate during the closing Senior TT race.
Sidecar driver Dwight Beare, 27, and solo rider Paul Shoesmith, 50, died in separate accidents on the opening day of the TT races last week.
The races on public roads around the island off the north-west coast of England between Britain and Ireland have been run since 1907 and rank among the most dangerous in motorsport.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Including the Manx Grand Prix races, held later in the year, there have been more than 250 rider fatalities to date on the Snaefell course.
(Reporting by Alan Baldwin, editing by Ian Chadband)
