Radio was the first wireless device that worked in 1897 but there was a lot of work before that like Maxwell predicted existence of electromagnetic waves in the year 1867. Hertz proved the existence of EM waves etc. You can say that it is around us since 1897 but in fact it is around us a lot more earlier like in 1867. For complete history, visit the link below.
wireless.ece.ufl.edu
wireless.ece.ufl.edu