The 37-year-old has penned a five-month deal with The Sky Blues after being released by Real Oviedo.
Engonga agreed his release from Oviedo, after having talks with Coventry earlier this week.
The Spaniard has been included in Coventry's squad for their game with Watford on Saturday and could make his debut subject to international clearance being granted.
Meanwhile, young striker Jay Bothroyd has revealed that becoming a father has taken its toll on his performances with The Sky Blues.
The 20-year-old became a father for the first time a month ago and has been forced to make arrangements with his girlfriend, in order to get enough rest before matches.
Bothroyd told the Coventry Evening Telegraph that having a new-born baby has taken some getting used to.
Bothroyd said: "I have not been that pleased with my form in the last few games but I don't think the team have done too well, to be honest.
"I think the new baby is maybe taking it's toll a little bit.
"It is hard to get used to waking up in the night but I have worked out a new arrangement with my girlfriend whereby I do the shifts at the beginning of the week and she does it later in the week to make sure I am getting enough sleep and will be fresh for match days.
"I think becoming a dad has made me a bit more mature.
"I have got responsibilities now and can't go off gallivanting and stuff, so I have got other people to think about now rather than just myself."
