The pair are due to appear at Aberdeen Sheriff Court today after being transported by police to Scotland over the weekend.
The paintings, by Scottish Colourists George Leslie Hunter and Francis C.B Cadell, went missing from a lodge within the grounds of Candacraig House, Strathdon, in 2001.
They were the property of Harry and Liz Young, who ran a plant nursery in the walled garden at Candacraig, which Connolly bought in 1998.
Police Scotland said today two people had been arrested in the Burgas area of Bulgaria on a European Arrest Warrant.
A statement from Police Scotland said: “Police Scotland can confirm that two people have been arrested in relation to the alleged theft of two paintings from a property within the grounds of Candacraig, Strathdon, in July 2001.
“A 66-year-old man and a 60-year-old woman were both arrested in the Burgas region of Bulgaria on Thursday 26th May 2016. The arrests were carried out by police in Bulgaria after Police Scotland sought and was granted a European Arrest Warrant.”
The paintings were recovered in Delhi in 2006 after the Hunter piece, Still Life with Tulips and Fruit, appeared in a Sotheby’s sale catalogue.
Experts working at the Art Loss Register were then led to the Cadell, which features pink roses in a vase on a black table.
Mr Young, who also acted as the registrar of births, deaths and marriages in the Strathdon area, was gifted the works by his mother.
At the time of their disappearance from his lounge he estimated their value to be around £100,000 each and said they were too valuable to insure.
He said it was “marvellous” to have the works returned after they were discovered in India with the Cadell later sold on to raise some money.
It is understood the Hunter work was then sold at Christie’s in London in 2012 for £337,000.
Connolly owned Candacraig until 2014 when he sold it to American industrialist Marc Lino and his Peterhead-born wife Lynn, who rent part of the main house as a luxury retreat.
The comedian was a popular figure in the community and a regular attendee of the Lonach Highland Gathering. Many of his celebrity house guests, including Steve Martin and Robin Williams, would make an appearance at the summer event.