First recorded by The Drifters (US #16 1960).
Other hit version by Jay & The Americans (US #6 1968).
From the wiki: “‘This Magic Moment’ was composed by lyricist Doc Pomus and pianist Mort Shuman, one of their best-known songs, and was first recorded in 1960 by Ben E. King and The Drifters. In 1969, ‘This Magic Moment’ was covered by Jay and the Americans and reached the Top 10 on the Billboard Hot 100.”
Jay & The Americans, “This Magic Moment” (1968):