The Polish six-time Grand Slam champion lost in the quarter-finals of the Australian Open and tournaments in Doha and Indian Wells before a shock second-round defeat by Magda Linette in the Miami Open last month.
That prompted Swiatek to part ways with her coach Wim Fissette and hire Roig, who worked with her idol Rafa Nadal from 2005-22 and more recently with Briton Emma Raducanu.
"I'm really happy to start with Francis," Swiatek told a press conference in Stuttgart.
"I was basically looking for someone with a good eye, really technical, but also a person that is experienced enough to help me through some different kind of situations. I feel Francisco has lived through everything on tour.
"It's going really amazing ... I was able to find a new coach pretty fast, which is a positive thing because when you do that in the middle of the season, it's nice to have some security in that."
Swiatek, who has won four French Open titles on her favoured clay courts, began preparations for the Grand Slam that begins on May 24th with a training block at Nadal's academy in Mallorca under the watchful eyes of the Spaniard.
"I asked if it would be possible for him to come and maybe be some kind of inspiration, also hear some feedback from him," Swiatek said.
"It was a privilege to have him on court. I honestly didn't have many expectations because I know he's super busy and he has a lot of stuff to do, even though he always has different projects and everything.
"Now I'll continue with Francisco. He'll be the person that takes care of the whole process. That's the plan for now."