Yes, as a part of Spain, Tenerife is very firmly within the EU and its currency is the Euro. However, the island has VAT free status which means it falls outside of EU Customs allowances.
Are the Canary Islands still part of Spain?
Most of Spain's national territory is located on the Iberian Peninsula (which it shares with Portugal and Andorra) situated in the southwest corner of Europe. However the Canary Islands, the Balearic Islands, a few smaller islands and the cities of Ceuta and Melilla in North Africa are also territories of Spain.