Of course he was!
After mentioning his nationality a few days ago, I've received a couple of doubting emails. So here are the facts.
Handel was born Georg Friedrich Händel in Germany in 1685. He moved to London as a young man in 1710 and remained in Britain until his death in 1759.
From 1712 he was a permanent resident, becoming a naturalised Briton in 1727 by means of an Act of Parliament. This was not an easy process, but the only way for a foreign-born resident to obtain citizenship in those days. From this point he was unquestionably British, albeit German-born.
As far as Handel's handle goes, correspondence of the period sometimes refers to him as Hendel or even Hendle, suggesting he retained the German pronunciation. However from 1715 he adopted the anglicised spelling 'George Frideric Handel', and this became his legal name on his naturalisation as a British subject.
Read more about Handel here.