Richards is to become a senior adviser to the firm next year, offering mentorship to company managers.
Bateman is currently head of European equities and co-manager of the Schroder ISF European Large Cap fund, which over the last three years has returned 27.6% versus a peer average of 26.9%.
He will assume responsibility for Schroders' global equities teams around the world, with total assets of £173.1 billion.
Bateman said: 'The key to Schroders’ success in Equities under the stewardship of Nicky has been our strong team culture across the respective desks, underpinned by our robust investment processes.
'Active asset management and the delivery of outstanding investment performance for our clients is going to be more important than ever before. I look forward to evolving our equity business to ensure we remain a global leader in the years ahead.'
Richards was Fidelity International's group chief investment officer until she left to take a break from the industry in March 2010. She returned to Schroders in 2014, having begun her career at the firm.
She added: 'It has been a privilege leading Schroders’ global equities teams and working with such great talent over the past four years.
'I am excited to continue working with Schroders as a special adviser to mentor and advise Schroders’ leaders and managers.'