South African all-rounder Delport, 27, made 249 runs in the T20 Blast and One-Day Cup for the Foxes this season.
Pace bowler Griffiths, 22, is currently on loan at Division One side Hampshire.
"It is important to strengthen the squad with white-ball cricket being played in blocks in 2017," chief executive Wasim Khan said.
"Cameron made a big impact when joining us this year and we're really pleased that he will be coming back to play for us in 2017."
Griffiths has played seven T20 games and made five List A appearances, but is yet to make his first-class debut.
Khan added: "Gavin was extremely impressive making his T20 debut for Lancashire in testing circumstances and has also made an impact while on loan at Hampshire, so we're delighted that he is joining us.
"He's only 22 and has had a good upbringing at Lancashire, so we're looking forward to Gavin continuing his career development with us at the Fischer County Ground."
Leicestershire have re-signed Cameron Delport for white-ball cricket in 2017 and signed bowler Gavin Griffiths on a two-year deal from Lancashire.