Ms Rodriguez made headlines in Ecuador in 2013 when she was the first transgender candidate to run for Government.
The couple decided to be just as public with their relationship, sharing pictures on Facebook.
Then they decided they wanted a child, and Mr Machado soon made the discovery he was expecting.
The couple were able to have a baby because neither had undergone corrective surgery.
Comment: So basically, a man who dresses as a woman and a woman who dresses as a man had a baby together. Hardly a feat of science but certainly indicative of the transgender mania that is sweeping the world.
Posting a photograph of their new son on Facebook, the couple wrote: "Our son is not only a blessing, but he also promotes love."
Ms Rodriguez, who was born a man named Luis, said: "We don't have a name yet, or rather we do, we are just waiting to announce it.
"Being a mother was never something I thought I would do because I am a transsexual.
"The law before demanded that to be recognised as a woman you had to be castrated.
"We are the same as other families. Even though we might not have the same rights, we're the same."
The new parents have previously spoken of her struggle after coming out to her family about her sex change.
Ms Rodriguez said: "We live as man and woman. I'm a transfeminine woman and Fernando is a transmasculine man. The process to get here was complex for each of us.
"Knowing it's our right, we decided to add another member to our family."
Comment: This has more to do with basic biology than with any notion of rights. Here's another story of basic biology being touted as a transgender scientific paradigm shatterer. 'Pregnant' man stuns medical profession
Mr Machado said that when he discovered he was pregnant, he "started crying with happiness, fear and dread".
He said: "I had never felt like that before. Wow, at last, I am completely happy."
The pair are one of the most high profile transgender couples in South America.
Reader Comments
Comment: So basically, a man who dresses as a woman and a woman who dresses as a man had a baby together. Hardly a feat of science but certainly indicative of the transgender mania that is sweeping the world.
So if I wear a big wig and earings my penis doesnt exist anymore????
If this wasn't so sad, it would be laughable. What's the point of all this oohing and aahing over a basic and everyday occurrence?
We're really scraping the bottom of the barrel here folks, when this sort of nonsense is even considered news.
The apocalypse occurred twenty years ago and most people missed it. We are all now in hell and these two are now our ambassadors to the other levels of hell which we have yet to visit.
Pack your bags people, its going to be a long and bumpy ride.
The miracle of birth happens every day 24/7 on this planet in the thousands. Now because a transgender couple has given birth, are we supposed to accept this as a normal human occurrence, which IMO it is not.
Makes me wonder how this will affect the child, and the imprinting upon that child as they grow up. How can you explain to a child, that a person who has the appearance of a male, behaves in a masculine way is actually there birth mother, and vice versa for the mother, looks like a female acts like female but is actually the father.
That takes a lot of explaining IMO are we are looking at a revision of human biology. It is known in seahorses, males are the ones that carry and birth the next generation. Thing is humans are supposed to be far more evolved. Makes me wonder.