Canadian-owned site AshleyMadison.com, with its tagline "life is short, have an affair", said it was listing in Europe because of the continent's "more laissez-faire attitude" to infidelity.
Parent company Avid Life Media said it hoped to raise $200m (Â£134m) in London later this year.
The site says it has 36 million members in 46 countries worldwide.
It claims to be the second-biggest dating website in the world, behind Match.com, and boasts of being "the most famous name in infidelity and married dating".
Reports suggest the site had $115m worth of sales last year.
Avid Life also owns CougarLife.com and EstablishedMen.com.
"In Europe, we have simply got a more laissez-faire attitude towards businesses such as ours," said Christoph Kramer, director of international relations at AshleyMadison.
A dating website focusing on adultery has announced its intention to list publicly in London.