The departures leave a significant hole in the Kames fixed income team, the duo acting as co-managers on six vehicles as well as leading the wider bond team.
Kames said Stephen Snowden and Adrian Hull will become co-heads of fixed income.
Mr Roberts co-managed the Kames Sterling Corporate Bond and Strategic Bond funds, and equivalent offshore strategies.
Mr Milburn managed the Kames High Yield bond, and also worked on the £380m Strategic Bond fund and offshore funds.
Alex Pelteshki, who joined Kames in 2014, will now become co-manager on the Strategic Bond fund alongside Juan Valenzuela. The fund has struggled in recent times, sitting fourth quartile over three and five years.
As part of Kames' offshore line-up, Mr Milburn will be replaced on the High Yield Global bond fund by Jack Holmes.
Chief executive Martin Davis said: "I would like to thank both David Roberts and Phil Milburn for their contribution...[and] congratulate Stephen and Adrian on their new roles."
"We are well placed to continue to grow our business and maintain our impressive record in managing fixed income investments for clients."
