The Republican head of the Senate Judiciary Committee has curtailed one of the last legislative limits on a president’s power to shape the federal courts, giving Donald Trump more freedom than any U.S. president in modern times to install his judges of choice, legal experts said.

Last week, Sen. Chuck Grassley (R., Iowa) reined in a tradition that empowered senators to block federal appeals-court nominees from their home state. His decision came about four years after Democrats, citing Republican filibusters of President Barack...