Because of the way dictionaries are compiled, it's difficult to know how to count words. But Merriam-Webster, which is the biggest and most comprehensive US dictionary, says that the Third New International Dictionary contains 470,000 entries; and they say that they added "well over 1,000 words" in 2018.
However, it is estimated that very well educated, literate English speakers only have a vocabulary of about 40,000 words.
Part of the reason why English has so many words is our dual heritage from Anglo-Saxon and Latin. Another reason is that for centuries, English dictionaries have been compiled "on historical principles," meaning that they feel that their job is to record the language as it is, not say what it ought to be, and thus they have been fairly open to including loan-words from other languages, and new coinages.