The Thai star will go on loan for one season from July onwards, with Almeria sporting director Alberto Benito Castaneda declaring him to be a "great choice" for the La Liga strugglers, who are currently battling the drop.
Speaking after the signing ceremony, Teerasil stated that he did not feel any pressure to succeed in Europe.
"I'm no superstar, not even close," he said. "So there's no pressure to trouble me."
"I still have tons of work to do, lots of things to learn, to polish as a professional player. I have to be open to anything that lies ahead."
The 25-year-old's father, Prasit, was delighted with his son's achievements and urged him to give his all without any reservations.
"Now I'm happy as we always wanted him to play in Europe for a team that is really interested about him in a footballing aspect, not just for marketing purposes," he said.
"This is the chance and he must take it. Even if they offer less money than he got from Muangthong, he still must take it."
Teerasil's agents, brothers Alejandro and Adrian Gil, revealed that negotiations with Almeria had started since November last year, after they were first impressed with him while surfing Youtube videos.
"We saw him for the first time five years ago and we have adored him since," they told Goal.
"Fortunately, the deal is done. We believe he can adapt himself to Spanish football just fine."