Seven-time NASCAR Cup champion Johnson switched to IndyCar for the 2021 season with Chip Ganassi Racing, contesting a road and street course-only schedule.
However the 46-year-old has pledged to contest the full season in 2022, including on ovals - having missed the Indianapolis 500, Texas and Gateway last season, and never competed at returning venue Iowa in NASCAR.
Johnson's best finish to date is a 17th, achieved in the Laguna Seca and Long Beach races that concluded the 2021 campaign.
Unser, who won two Indycar titles and claimed Indy 500 victories in 1992 and 1994, also has experience of stock car racing having won the IROC championship against some of NASCAR's top names in 1986 and 1988.
Speaking to Autosport for a podcast promoting his recently-released book, A Checkered Past, Unser said Johnson's steep learning curve will soon be rewarded with strong results in IndyCar, and expects that "it's going to be like a light switch".
"Jimmie has shown the world how competitive the Indycars are, it's that simple," said Unser.
"He's a super-talented driver, and so he's just proving, 'Hey, it's tough out here'.
"He's got a great team, great coaches, great engineers, they're all working together in that Ganassi camp.
"For me, it's just a matter of time. and once it happens with Jimmie, it's going to be like a light switch. All of a sudden it's going to go off and he's going to be running up in the top five, no problem.
"But, it takes a while to get there and it just shows how competitive IndyCar racing is."
Johnson, who was lapped on his way to finishing 23rd in the St Petersburg season-opener last month, backed himself earlier this year to be "much more competitive" on ovals.
Although the dynamics of racing a single-seater on an oval differ vastly to that of a stock car, Johnson remarked that he was “surprised how familiar it felt” driving the Texas oval in testing.
Unser said he believes Johnson's years of experience on ovals will prove useful.
"Experience is experience in race cars, it doesn't matter what the race car is," he added.
