Morgan, who previously played for Celtic and St Mirren, has been drafted in to bolster Clarke's injury-hit attack.
Liverpool's Ben Doak and QPR's Lyndon Dykes have been forced to withdraw from the squad due to injuries over the past week.
Morgan won his only two Scotland caps against Peru and Mexico in 2018 but now has a chance to secure a place in Clarke's final group for the tournament in Germany.
"Steve Clarke has bolstered his squad with the call-up of Lewis Morgan. Welcome back to the squad," Scotland announced on X, formerly known as Twitter.
Morgan is the second Scotland attacker to be called up this week after Bristol City striker Tommy Conway was promoted from the Under-21 squad on Tuesday.
Clarke's squad is now up to 28 but it will be trimmed to 26 by Friday evening after the home friendly against Finland.
Scotland face hosts Germany in the opening match of Euro 2024 in Munich on June 14 before facing Switzerland and Hungary in their other Group A fixtures.
The Scots have looking to make it past the group stage of a major tournament for the first time.
