This is a love song written by John Dowland. Dowland (c1563-c1626) was England's pre-eminent lutenist and composer, and quite likely the first singer-songwriter as we would understand the term. Dowland's origins are uncertain, although he was probably born in Westminster; he was a Catholic, traveled extensively, and was welcomed at the courts of kings. He was renowned for his beautiful melodies.
Dowland's music is all but unknown today outside of classical circles, but in 2006 Sting put out Songs From The Labyrinth, a collection of Dowland compositions, including this song.
The English language has changed somewhat since Elizabethan times; according to Dowland biographer Diana Poulton, the first line of the song reads: "Come againe: sweet loue doth now euite."
Suggestion credit: Alexander Baron - London, England, for all above