Elise Tan-Roberts, who can also recite the phonetic alphabet and count to 10 in Spanish, has an IQ of 156.The rating makes her smarter than former Countdown maths whiz and fellow Mensa member Carol Vorderman.
The toddler's other feats include spelling her name aloud, reading the words mummy and daddy, naming all three types of triangle and reciting the normal alphabet.
Mensa welcomes the top 2% of the population based on IQ. It normally only tests children aged 10 or above, but the society accepted Elise's membership based on an intelligence measure.
Child psychologist Professor Joan Freeman used the Stanford-Binet Intelligence Scale test, which found she was in the top 0.2% of her age in the country.
Mensa chief executive John Stevenage said: "(Elise's parents) now realise they have an interesting challenge on their hands as she grows up."
Elise's mother Louise, 28, from Edmonton, London, said she realised her daughter was different as soon as she was born.
She took "an unusual" interest in her surroundings, uttered her first word aged just five months and took her first steps at eight-and-a-half months.
The mother told the Daily Mirror: "She just says things and you have no idea where she got it from."
Prof Freeman said the child's memory was her great gift.
The psychologist was "extremely impressed she was able to reel off the capital cities" and the phonetic alphabet.
Mensa has about 24,000 members in the UK and Ireland - about 900 of whom are aged under 18.
As well as Carol Vorderman, whose IQ is 154, other famous members include DJ and TV presenter Sir Jimmy Savile and inventor Sir Clive Sinclair.
