Johnson, 19, decided to go pro after his freshman season at Minnesota in which he totalled four goals and 20 assists in 41 games. He turned down a chance to join the Blues for the final few regular-season games right after Minnesota fell one game short of the NCAA Frozen Four in St. Louis, but changed his mind a few weeks later.
The Blues envision Johnson as one of their top six defencemen next season.
"We are very excited about Erik's decision to join our club next season," team president John Davidson said. "We wanted to give Erik the proper time to make the best decision for himself and his family."
Johnson, 6-4 and 222 pounds, will play for Team USA at the IIHF world hockey championship in Moscow from April 27-May 13.
He played for the U.S. in both the 2006 and 2007 world junior championships.