The 44-year-old was promoted to the role on Wednesday after cricket manager and former player Robinson was appointed England women's head coach.
Davis made his Sussex debut as a player in 2001 before becoming second-team coach and later assistant coach.
"I learnt a lot from Mark Robinson, but my coaching style will certainly be different," he told BBC Sussex.
Davis takes over a side who were relegated from County Championship Division One last season and will report to a new director of cricket - a post Sussex are hoping to fill in the months ahead.
"Mark Davis' appointment is in keeping with the Sussex tradition of promoting from within. He served a long apprenticeship under the guidance of Mark Robinson.
"The priority will be to secure a prompt return to Division One of the County Championship, while also improving their form in one-day competition.
"His partnership with new captain Luke Wright could usher in an exciting new era for the club."
"I've known the players for a long time and I think that will be a benefit for me," he said.
"I'll take a lot from what 'Robbo' did before me and also Peter Moores, who I played under when he coached here. But I'm very clear in the way I'm going to move this squad forward.
"We were pretty unlucky with injuries last year, but we didn't play well enough and that's why we are where we are.
"It's a great chance to develop a team going forward that can hopefully get promoted, but also compete at that level."
Davis was part of the Sussex side which won the club's maiden County Championship title in 2003 and went on to take 188 wickets with his off-spin, as well as scoring more than 2,000 runs across all three formats.
Robinson, who led Sussex to two County Championship titles and four one-day trophies, has backed Davis to lead the club back to the top division of first-class cricket.
"Mark is different to me, with different strengths and qualities," Robinson told BBC Sussex.
"His values are good, his integrity is high and he will supplement and work well with (newly appointed captain) Luke Wright.
"I'd have loved to have left them in Division One, but the margins are really small. I'm convinced they'll go back up next year as there are a lot of great things happening behind the scenes."
New Sussex head coach Mark Davis says his style will be markedly different from that of predecessor Mark Robinson.