Before joining Women’s Aid, Neate was executive director of external relations and communications at Action for Children, where she worked for seven years. She previously worked as a journalist.
"It’s an honour to join a pioneering organisation that I’ve long admired to help take its work to the next level," said Neate.
Sir Derek Myers, chair of Shelter, said Neate’s "impressive expertise and fresh thinking will help the organisation develop and implement a range of exciting services and ground-breaking campaigns".
Beverley Pass, co-chair of Women’s Aid, said Neate had done a "fantastic job" for the charity over the past four years.
Neate will be paid £122,500 a year for her new role, which a Shelter spokeswoman said was at the start of the charity’s chief executive pay scale.
Robb was paid £133,843 a year, according to the charity’s annual report covering the year to the end of March 2016.
Graeme Brown, chief executive of Shelter Scotland, who has been interim chief executive of Shelter since Robb’s departure, will continue in the role until Neate takes up the job on 14 August.