Storey, 39, became Great Britain's most successful female Paralympian at the Rio Games, winning her 14th gold medal.
Cundy, one year younger and like Storey an ex-swimmer, has seven Paralympic golds - four in cycling.
The Great Britain team will compete in both track and road World Championships this year.
The track event takes place in Los Angeles from 2-5 March while Pietermaritzburg, South Africa will host the road event from 31 August-3 September.
The 23-strong squad does not include dual-sport star Kadeena Cox, who has had her UK Sport funding suspended while she takes part in the Channel 4 winter sports show The Jump.
Other Rio gold medallists included are Megan Giglia, and the tandem pairings of Sophie Thornhill and Helen Scott, Steve Bate and Adam Duggleby, and Corrine Hall and Lora Fachie. Handcyclist Karen Darke also makes the squad, as do Louis Rolfe and Jon Allan Butterworth, who won team sprint gold alongside Cundy.
London 2012 rowing gold medallist David Smith remains on the squad as he continues his rehabilitation from surgery on a spinal cord tumour.
At the Games in Brazil, ParalympicsGB cyclists topped the medal table, winning 21 medals, including 12 golds.
Head coach Jon Norfolk, said: "The squad we've named is full of Paralympic and world champions as well as a number of riders who we believe have the potential to improve and become medal-competitive over the next four-year cycle."
Squad: James Ball, Steve Bate, Jon Allan Butterworth, Jody Cundy, Karen Darke, Hannah Dines, Adam Duggleby, Lora Fachie, Neil Fachie, Megan Giglia, Jon Gildea, Corrine Hall, Crystal Lane, Craig Maclean, Pete Mitchell, Simon Price, Louis Rolfe, Liz Saul, Helen Scott, Dave Smith, David Stone, Sarah Storey, Sophie Thornhill
Rio Paralympic gold medallists Sarah Storey and Jody Cundy have been named in the Great Britain Para-cycling squad for 2017.