Sir Ringo Starr's son Zak Starkey has married his longtime partner Sharna 'Sshh' Liguz

The lovebirds - who chose their 12-month-old daughter Luna Lee Lightnin's birth date to get hitched - were given away by Ringo, 81, and Sharna's father Andrzej Ligu.

Pearl Jam's Eddie Vedder and Johnny Marr were Zak's best men, though the former Smiths rocker couldn't be there in person and was seen appearing via video call on a tablet.

Reggae star Pato Banton officiated the ceremony, the first of two, with further plans to celebrate in Jamaica and the UK.

In a statement issued to PEOPLE, the couple said: "After 18 years together, Luna's umbilical cord kinda tied the knot but we wanted to make it official and share with our friends and family in the U.S., before doing the same in Jamaica and the UK."

The bride wowed in an Alexander McQueen gown, while Zak donned a summery yellow suit with a contrasting bold red shirt.

Over on Instagram, drummer Zak, 56, thanked their guests for sharing their special day and experiencing "true party stamina"

He captioned a picture of an invite: "Great to be solid with the greatest girl in the world. And to celebrate Luna's No. 1 birthday. Thanks to everyone who came from near, far, wide, abstract and online.

"Our dearest friends in da USA- great to see u at our wedding and experience true party stamina. Feels great to be wed to the woman I have loved for 18 years. (sic)"

Sharna - who is part of the musical duo Sshh with her now-spouse - wrote on her own page: "This super small affair happened with our nearest dearest on the day our darling daughter was born.

"A double celebration of love life all the blessings bestowed upon us. So grateful for our family. Locked and loaded ready to roll with love."

Ringo - who was joined at the wedding by his wife Barbara Bach - also has son Jason, 54, and daughter Lee, 51, with Maureen.