William and Kate were greeted by Health Secretary Matt Hancock.
It's the royal couple's first joint public duty since Kate gave birth to Prince Louis on 23 April.
The Mental Health Summit will see political figures, leading academics and policy-makers from around the world come together with one common goal: better mental health for all.
They also heard presentations on two case studies of active mental health programmes from Slovenia and the United States of America and visited an exhibition area.
Kate, 36, who studied History of Art at St Andrews, where she first met her husband, laughed and took the brush from Mr Vargas, asking him: 'Where can you hide it?' Mr Vargas pointed to a shoulder area and Kate made her brushstroke - as William joked: 'It's nearly ruined the picture'.
"That's pretty much ruined the picture", William teased his wife before poking fun at himself.
The event is the Duchess of Cambridge's second royal engagement since returning to work following the end of her maternity leave.
The Duke and Duchess of Cambridge have arrived at a summit in London aimed at helping to improve mental health around the world.
'You are allowed to go anywhere, ' encouraged Kate, who was wearing a £1,500 bespoke lavender Emilia Wickstead dress - previously seen on the couple's 2017 tour to Germany - with £510 Gianvito Rossi nude heels.
Catherine - who also has children Prince George, five, and three-year-old Princess Charlotte - then praised the artist for his work. He has since been joined by wife Meghan Markle at mental health charity events.