They went on to receive Rs. 1.5 crore for Ashwin and also got Karnataka spinner Jagadeesha Suchith in return.
This ended a series of serious negotiations between the two franchises.
Ashwin captained KXIP for two seasons and now moves to Shreyas Iyer-led DC.
Key info about the deal
The report added that KXIP were also looking to get Kiwi speedster Trent Boult as part of the deal but that did not materialize.
Ashwin is expected to be paid Rs. 7.6 crore by the Delhi Capitals, which is his auction value.
Meanwhile, a formal announcement will be made before the IPL transfer window closes on November 14.
Everyone is happy with this deal, says Ness Wadia
"Everyone is happy with this deal. We are happy, Ashwin is happy and Delhi is happy. We were in talks with three teams but have finally come to this conclusion. We wish Ashwin the very best," KXIP co-owner Ness Wadia told PTI.
DC set to bolster the side by getting Ashwin
DC were interested in the prospect of getting Ashwin to bolster the side.
They are a young team and Ashwin will help with his experience.
DC have many spin options and Ashwin will be another strong addition.
The former Chennai Super Kings player had joined KXIP for a sum of Rs. 7.6 crore in 2018.
He brings experience and quality in the ranks.
A look at Ashwin's IPL career and stint at KXIP
Ashwin has picked up 125 scalps in 139 IPL matches so far.
He averages 26.48 and has an economy-rate of 6.79.
In his two-season spell at KXIP, the premier spinner accounted for 25 wickets.
Under his captaincy, Kings XI won 12 games and lost 16 in the previous two seasons.
On both occasions, they lost the plot after showing a lot of promise.
DC overloaded with spin options
DC already have a pool of spinners. They had earlier roped in Mayank Markande from Mumbai Indians.
They also have the likes of Axar Patel, Sandeep Lamichhane, Amit Mishra and Rahul Tewatia.
Getting Ashwin brings more depth for this side.
However, it remains to be seen how they manage the spin options.