Parker takes over from Bruce Macnaughton, who is leaving The Gytes after five years.
Parker, who coaches the Scottish women's squad and was previously with Biggar, Melrose and Gala, will speak to the players before taking any firm decisions, but his former Gala colleague, Richie Gray, is expected to be invited to join him.
"This is a real family club and there is an edge about it. That is what appealed to me. This move felt right. I have missed the weekly commitment to training," Parker said.
Parker made his announcement at the Peebles Sevens at the weekend when Melrose retained the cup with a 54-7 win over Jed-Forest in the final.
The Dodds brothers, Allan and Graham, shared the early scores with Calum Anderson and Lewis Young replied for Jed. Allan Dodds stretched the lead in the second-half and Calum Anderson, Jamie Murray and Malcolm Clapperton added further scores.
Kelso, who lost to Selkirk, broke their duck after two successive final defeats by winning the Langholm Sevens on Saturday at Milntown for the first time since 1997.
The Tweedsiders won a pulsating final by 36-33 against Edinburgh University, scoring the crucial try through Mee Kaa Eel Hartley in the final move of the game. Hartley also scored the first try while the other touchdowns came from Andrew Haig (2) and Chris Kellington (2) with Ewan Ford adding the conversions.
The University scores came from James Walkingshaw (2), Daniel Mays and James Niblock.
In the Kings of the Sevens Series, Kelso still lead with 38 points from Jed-Forest and Selkirk.