The company said Svanström brings "significant" experience of growing established business to business to consumer online marketplace businesses.
Following his appointment as Global President of Hotels.com and Expedia Affiliate Network brands in 2013, he served on the Expedia Group global leadership team and over five years grew revenues to more than $3bn and led direct teams of 1,500 people across four continents, Rightmove said.
Brooks-Johnson will continue to lead the business and support an orderly transition until after the presentation of the 2022 full-year financial results. Svanström will join the company on 20 February 2023 as executive director and CEO designate and will be appointed CEO on 6 March 2023.
Rightmove said it continues to make good progress with the implementation of its strategy and that trading in the year to date has been as expected. Its expectations for the full year remain unchanged.
Chair Andrew Fisher said: "I would like to thank Peter for his outstanding leadership as CEO over the past five years and for his significant contribution to the company throughout the past 16 years.
"Under his leadership the company has significantly increased value for our customers and home hunters, with time spent on Rightmove increasing from 11.7bn minutes in 2016, to over 18bn in 2021. This has delivered sustained growth for our shareholders, increasing annual revenues from £220m to £304m in the same period and returning more than £750m through dividends and share buybacks."