The overall commander of US (and Allied) forces in the West was Dwight Eisenhower (who was later President). Lt. Timmerman drove the first tank over the bridge at Remagen (the first crossing that hadn't been destroyed by the retreating Germans), who was part of General Hoge's command. Though it wasn't in 1944, but on 7/3/1945.
The first major incursion into Germany was at the town of Aachen (which happened months before Remagen). This was the US 1st army, which was led by the very excellent General Courtney Hodges. He wasn't as flamboyant as Patton or Monty, but he got the job done.