First released by John Michael Montgomery (US #42/C&W #1 1993).
Hit version by All-4-One (US #1/R&B #13/UK #2/CAN #1/AUS #1/NETH #1 1994).
http://youtu.be/16yarf4ZCwA
From the wiki: “‘I Swear’ was written by Gary Baker and Frank J. Myers, who also recorded a demo of it in 1989 at Fame Studios in Muscle Shoals, Alabama. They couldn’t convince anyone to record the song at the time but, in 1992, they recorded a new demo of ‘I Swear’ which attracted the attention of John Michael Montgomery. Montgomery would record the song in 1993 and release it as the first single from his 1994 album Kickin It Up.