There is a catch, however.
The nanny will be expected to help homeschool the boys and take care of their baby sister, Wren, as well as generally assisting with cooking and cleaning.
"It's hard to define your exact hours because you will be living with us, but you will have time to yourself every day for sure, and one to two times a week you'll be able to go off on your own and have your own adventures," M'Kenzie said in the video.
The Tillotsons will pay a monthly salary of US$1200-1500, which is about AU$1600-$2100, and although that includes living and travel costs, a number of Facebook users have pointed out it's actually incredibly low.
"If you're a child-care worker interested in travel, protect yourself from this kind of unethical and illegal work, and go through an agency who protects both the employer and employee," one user wrote.
"$1200-1500 a month? For cooking, cleaning, and homeschooling their children? Psh. That's not a good deal. I realise you get to travel the world but that is not good pay for all they are asking you to do," one user wrote on Facebook.
"They're not expected to do all the cooking and cleaning," M'Kenzie replied.
"But we're looking for someone to 'pitch in' in general as we're living in the same space. Our nanny will get two days off a week and obviously time to themselves daily. Not looking for a Cinderella!"
The deadline for applications was originally set for January 17, however, the cute video went viral on Facebook, amassing some 7.6 million views.
Despite the low wage, the couple received so responses they decided to close applications this morning.
"We've had so many awesome people respond, and it has seriously touched us," Derek said in a Facebook live video.
"When we initially started this search, we honestly expected maybe someone from a different town, or maybe one of our friend's friends would be the perfect match for us.
"We were talking about this before ... and we were like, 'Imagine if our video gets 10,000 views, imagine if we have a thousand applications to choose from, you know?
"We've just been blown away by the interest."
The couple will work throughout the trip, running their successful product distribution company, and they'll also sell their house.
So far, applicants have included teachers, nurses, social workers, and even medical doctors.
In their Facebook live video, the couple laughed that many applicants are better qualified to look after their children than they are.
However, overall the reaction has been incredibly positive.
"I hope I get picked but if not this is just such an exciting and amazing thing to do. Good luck everyone!" one user wrote on Facebook.
"Whoever gets this amazing opportunity is going to get the experience of a lifetime," wrote another.
"What a cool experience for the chosen person. Thank you to this family for creating such an amazing opportunity."
You can apply to join the waitlist on their website.
