Trump Jr. is dating socialite Bettina Anderson after they were first seen holding hands together last August.
He was engaged to former Fox News anchor Kimberly Guilfoyle and their split became public last November.
“Love is in the air and life is better with you by my side!” Woods wrote. “We look forward to our journey through life together. At this time we would appreciate privacy for all those close to our hearts.”
Vanessa re-shared it to her Instagram Story.
“So happy for you both ! 🥰🥰,” her former sister-in-law, Ivanka Trump, wrote in the comments of Woods’ post.
The 15-time major champion is friends with President Trump and they enjoyed a round of golf at Trump International Golf Club in Palm Beach earlier this month.
Woods and Vanessa had been the subjects of romance buzz for some time before he confirmed Sunday they are dating.
The golf legend was seen with Vanessa and her 17-year-old daughter, Kai Trump — who committed to the University of Miami golf team last summer — at various events this past month, including the Genesis Invitational at Torrey Pines Golf Course in La Jolla, Calif. on Feb. 16.
The mother-daughter duo supported Woods at a TGL event in Florida, as seen in a video posted to Kai’s Instagram.
Woods’ children, daughter Sam, 17, and son Charlie, 16, are enrolled at The Benjamin School in Palm Beach, along with Kai. Tuition at the private institution for grades 9-12 runs at 38,595.
The Post confirmed Woods and Vanessa are quietly dating and taking things slow after their friendship blossomed into “something more.”
Woods and his ex-wife, Swedish model Elin Nordegren, were married for six years before their divorce in 2010.
It followed Woods’ infidelity scandal that played out in the public eye and nearly destroyed his career.
Earlier this month, Woods announced he underwent surgery after rupturing his left Achilles tendon while training at home.
Woods said he was back at home in Jupiter, Fla., and plans to “focus on my recovery and rehab.”