From Wikipedia:

Origins

 

A ticket to “Washing the Lions” in London from 1857. This traditional April Fools prank is first recorded in 1698.

In Chaucer’s Canterbury Tales (1392), the “Nun’s Priest’s Tale” is set Syn March bigan thritty dayes and two. Modern scholars believe that there is a copying error in the extant manuscripts and that Chaucer actually wrote, Syn March was gon. Thus the passage originally meant 32 days after March, i.e. May 2, the anniversary of the engagement of King Richard II of England to Anne of Bohemia, which took place in 1381. However, readers apparently misunderstood this line to mean “32nd of March,” i.e. 1st April. In Chaucer’s tale, the vain cock Chauntecleer is tricked by a fox.

In 1509, a French poet referred to a poisson d’avril (April fool, literally “April fish”), a possible reference to the holiday. In 1539, Flemish poet Eduard de Dene wrote of a nobleman who sent his servants on foolish errands on the 1st of April.  In 1686, John Aubrey referred to the holiday as “Fooles holy day”, the first British reference.  On 1st April, 1698, several people were tricked into going to the Tower of London to “see the Lions washed”.  The name “April Fools” echoes that of the Feast of Fools, a Medieval holiday held on the 28th December.

In the Middle Ages, New Year’s Day was celebrated on the 25th of March in most European towns. In some areas of France, New Year’s was a week-long holiday ending on the 1st of April^. So it is possible that April Fools originated because those who celebrated on the 1st of January made fun of those who celebrated on other dates. The use of the 1st of January as New Year’s Day was common in France by the mid-sixteenth century, and this date was adopted officially in 1564 by the Edict of Roussillon.

In the eighteenth century, the festival was often posited as going back to the time of Noah. According to an English newspaper article published in 1789, the day had its origin when Noah sent his dove off too early, before the waters had receded; he did this on the first day of the Hebrew month that corresponds with April.