The former tennis pro took to Instagram on Thursday to post a video of 2-year-old Lucy and Nicholas smiling as they run happily on a field of green grass.
Kournikova, 38, chose a fitting song for the cute video's soundtrack — her husband's 2012 heartfelt hit "Finally Found You."
She hashtagged the post #happynewyear, adding the phrase a second time in her native Russian.
Fans rarely get to see images of Lucy and Nicholas since the ultra-private couple welcomed them in December 2017.
In August 2018, Iglesias, 44, took time out from his "All the Hits Live" world tour to share a video of himself acting goofy to delight his then 8-month-old children.
In the clip, the Grammy winner ran back and forth while making silly sounds to earn a few giggles from Lucy and Nicholas, who watched him from their stroller.
"Tough audience to entertain," Iglesias quipped in the caption.
The "Bailando" singer also showed off his dad humor the month before when he shared a video of himself in a pool with little Lucy. In that clip, Iglesias sucked pool water into his mouth and then sprayed the water out to delight his baby daughter.
Not only does the couple — who began dating in 2001 — keep their family life private, they also managed to keep Kournikova's pregnancy a secret from fans.
However, once their babies arrived, neither could keep their happiness under wraps.
Iglesias soon shared a photo of himself nuzzled close to one of his bundles of joy and simply captioned the shot, "My Sunshine."
Kournikova used the same caption for her own blissful pic with one of her babies.
Iglesias also opened up — just a little — about how much he loves being a father during an interview with British TV host Vick Hope in October 2018.
"It feels incredible. It's one of the best feelings in the world," the singer gushed, adding, "I wake up in the morning and I'm like, 'I'm a dad.'"