FreeForexAPI
Real-time foreign exchange rates for major currency pairs
Exchange rates for 144 currencies with daily history back to the 1990s, English and Arabic.
Fulusly API is a free Currency Exchange API that requires no API key, is served over HTTPS and supports CORS, so it can be called from the browser.
Free currency-rates JSON API and an embeddable converter widget from Fulusly.
Details from fulusly.soft9.us.

Unified API suite · now live
Geocode an address, validate an email, track a flight or pull stock data with one account, one dashboard and one API key.
Real-time foreign exchange rates for major currency pairs
Iran free-market USD, EUR, CNY, gold and coin rates in toman, live and daily archive since 2010
The Fulusly API is provided by Fulusly (fulusly.soft9.us). Free currency-rates JSON API and an embeddable converter widget from Fulusly.
Yes. The Fulusly API is listed in the Currency Exchange category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
No. The Fulusly API requires no authentication, so you can start making requests without signing up.
Yes. The Fulusly API supports CORS, so front-end JavaScript can call it directly.
Yes. The Fulusly API is served over HTTPS, so it's safe to use in production.