Mr Jammeh told state TV the proclamation was in line with Gambia's "religious identity and values".
He added that no dress code would be imposed and citizens of other faiths would be allowed to practise freely.
Some 90% of Gambians are Muslim. The former British colony's economy relies heavily on tourism.
However, relations with the West have soured recently.
The European Union temporarily withheld aid money to Gambia last year over its poor human rights record.
Mr Jammeh has been president of the tiny West African country for 21 years.
"As Muslims are the majority in the country, the Gambia cannot afford to continue the colonial legacy," Mr Jammeh told state TV, explaining his decision to proclaim an Islamic republic.
Other Islamic republics include Iran, Pakistan and - in Africa, Mauritania.
Mr Jammeh withdrew Gambia from the Commonwealth in 2013, describing the organisation as neo-colonial.
In 2007, he claimed to have found a herbal cure for Aids.
Gambian President Yahya Jammeh has declared his Muslim-majority country an Islamic republic, saying the move marks a break with the colonial past.