The Westron speech is derived ultimately from the Adûnaic tongue of Númenor, and originated on the western coastlands of the continent of Middle-earth. From there, it spread to most of the lands through which the action of The Hobbit and The Lord of the Rings passes, with the notable exception of Mordor.
In The Hobbit and The Lord of the Rings, Westron was completely translated by English. This had certain important implications: first of all, proper names with derivations somewhat evident to speakers of Westron had been translated, to preserve the effect. Thus, names like Baggins, Bagshot Row, Peregrin, Rivendell etc., are not the actual names. (For example, Meriadoc Brandybuck's actual first name is supposed to have been 'Kalimac'. 'Meriadoc' is designed to maintain the reference to merriness contained in the original name Kalimac.) The ending of the 'true Hobbit' names Bilbo and Frodo was also changed: in Westron they were Froda and Bilba, but Tolkien changed this to -o because -a is usually a female ending in English.
The translation went one step further by also changing all English-related languages: Rohirric, the language of the Rohirrim was translated by Anglo-Saxon, because Rohirric resembled an ancient form of Westron like AS is an ancient form of English, and the tongue of Dale, where the names of the Dwarves of Durin's house came from, was translated by Old Norse, a language related to AS and modern English as Dalish was related to Rohirric and Westron.