A source said Tieszen was attempting to help his brother-in-law, Brent Moline, 61, who had got into difficulties on the reef, when his kayak capsized.
Police emergency services were called and they recovered the bodies of both men.
The family will repatriate them back to the US. The daughter of one of the men told police they were in Rarotonga to attend a wedding.
A source also said the ceremony was due to take place later on the day of the tragedy.
Tieszen, from Rapid City, was in his first term in the State House of Representatives, after having served in the State Senate from 2009 to 2016. He had also served with the Rapid City Police Department, from 1975, serving as Police Chief from 2000 to 2007.
Expressions of remorse and condolence flooded onto social media Thursday afternoon as news of Tieszen’s passing spread.
“Craig Tieszen was a good man and a dedicated public servant, and his loss is very sad,” said the Governor of South Dakota, Dennis Daugaard in a statement.
Duagaard said he would order flags be flown at half-mast on the day of his funeral, the date of which has yet to be confirmed.
