The Roman poet Sextus Propertius gave us the earliest form of this saying in Elegies:
“Always toward absent lovers love’s tide stronger flows.”
The contemporary version appears in The Pocket Magazine of Classic and Polite Literature, 1832, in a piece by a Miss Stickland:
‘Tis absense, however, that makes the heart grow fonder.
As with many proverbial sayings there is another that expresses the exact opposite point of view – ‘out of sight, out of mind‘.
‘Absence makes the heart grow fonder’ was also source material for the lewd wordplay:
“Absinthe makes the fart grow stronger”.
See also: the List of Proverbs.