Mark Bitcon, 28, leaves his club post with the Warriors to take up the full-time Scotland job, and will be replaced at Glasgow by his former assistant, Gary Sheriff.
Having worked with Scotland on a part-time basis previously, Bitcon's appointment ahead of the RBS 6 Nations Championship and in a World Cup year has been welcomed by national team head coach Frank Hadden.
"Mark has played a key role in the improving fortunes of the Scotland team," said Hadden. "He is highly regarded by the players."