My understanding is that it was given to St. Dominic (1170-1221). However there may be a more complicated history to it.
Firstly, well before that, monks had a practice of praying the whole 150 psalms every day. However lay brothers in monasteries were illiterate and so they prayed the "Our Father" (Latin Pater Noster) 150 times using knotted cords to keep count. This practice spread to lay men and women and beads were used instead of knots. There is a street in London called Paternoster Row where these beaded cords were made
[A] possible etymology is that it was the main place in London where paternoster beads were made. The beads were popular with the laity, as well as illiterate monks and friars at the time, who prayed 50 Paternoster prayers (Latin for "Our Father") three times a day as a substitute for the 150 psalms recited a day by literate monks. (Wkipedia).
According to an article in This Rock magazine "The word "bede" in Middle English, from which we derive the word "bead," originally meant "prayer."
It seems to have evolved from the original given to St. Dominic as, again according to the This Rock magazine "During the fifteenth and sixteenth centuries the rosary settled into its present form. It now consists of the Apostles' Creed, the Our Father, the Hail Mary, and the Gloria."
According to the section on the Rosary in the Directory On Popular Piety And The Liturgy issued by the Vatican "The Rosary is essentially a contemplative prayer, which requires "tranquillity of rhythm or even a mental lingering which encourages the faithful to meditate on the mysteries of the Lord's life"