Isaac Tiharihondi is alleged to have brutally killed Revd Dr Israel Ahimbisibwe, 51, Dorcus Ahimbisibwe, 47, and Israel Ahimbisibwe Jr., 5, last week.
It's claimed he used a lamp, baseball bat and a hammer to kill his parents, before stabbing his little brother with a kitchen knife.
The 19 year old is also alleged to have fled Texas after the crime. He was arrested in Mississippi.
During an initial appearance in court he appeared calm and looked at the ground.
Revd Dr Ahimbisibwe was described as "beloved" by his congregation at the Church of the Redeemer Episcopal in Houston and leaves behind two other children.
"While I am relieved authorities have found Isaac, I am heartbroken that he has been charged with capital murder," said the Rt Revd C. Andrew Doyle, Bishop of Texas. "This only adds to the tragedy of their deaths and raises more questions than it answers," he said.
He added: "As a Christian community, let us pray for Emmanuel and Isaac as they journey through this time of grief and sorrow.
"Let us also pray for our courts and our prisons, that all involved will be given clarity of mind, peace and wisdom.
"Our Book of Common Prayer reminds us to 'pray that any that are held unjustly be released and that those who are guilty find repentance and amendment of life.'
"We follow a God in Jesus Christ who is present with those who suffer. Let us be faithful to the God of love and forgiveness".