The use of a seven-note diatonic musical scale is ancient, though originally it was played in descending order.
In the eleventh century, the music theorist Guido of Arezzo developed a six-note ascending scale that went as follows: ut, re, mi, fa, sol, and la. A seventh note, “si” was added shortly after. The names were taken from the first verse of the Latin hymn Ut queant laxis, where the syllables fall on their corresponding scale degree.

Sheet Music for Ut Queant Laxis

Ut queant laxis resonāre fibris
Mira gestorum famuli tuorum,
Solve polluti labii reatum,
Sancte Iohannes.

The hymn (The Hymn of St. John) was written by Paulus Diaconus in the 8th century. It translates as:
So that these your servants can, with all their voice, sing your wonderful feats, clean the blemish of our spotted lips, O Saint John!

“Ut” was changed much later in Italy to the open syllable Do, and Si was added to complete the diatonic scale. In Anglo-Saxon countries, “si” was changed to “ti” by Sarah Glover in the nineteenth century so that every syllable might begin with a different letter. “Ti” is used in tonic sol-fa and in the song “Do-Re-Mi”.
In the Elizabethan era, England and its related territories used only four of the syllables: mi, fa, sol, and la. “Mi” stood for modern ti, “fa” for modern do or ut, “sol” for modern re, and “la” for modern mi. Then, fa, sol and la would be repeated to also stand for their modern counterparts, resulting in the scale being fa, sol, la, fa, sol, la, mi, fa. This was eventually eliminated by the 19th century, but it was (and still is in a few rare circumstances) used in the shape note system, which gives each solfège syllable a diffferent shape.