The Belgian club had spent the summer pursuing Janssen but had been unable to thrash out a deal with Vitesse.
Janssen's fee was proving a stumbling block as Vitesse were demanding ‚é¼4 million for the former Dutch Under-21 international.
Genk were reticent to splash out more than ‚é¼1.5 million but the two clubs have now struck a compromise.
The 22-year-old will spend the season on loan at Genk with the Jupiler League side having the option to sign him on a permanent basis next summer.
Janssen was the preferred acquisition of Genk coach Sef Vergoossen, who had also put Vitesse duo Gert Claessens and Didier Martel under close scrutiny.
Despite Janssen's inability to secure regular first-team football, it did not deter Vergoossen from snaring the highly-rated midfielder.
Vitesse are now trying to sell Martel and Claessens with the latter having an offer from Genk's Belgian rivals Standard Liege.
