WASHINGTON—Donald Trump’s plan to nominate CIA Director Mike Pompeo to succeed Rex Tillerson as secretary of state positions a crucial Trump ally as the administration’s top diplomat, one who the president said is more in line with his foreign-policy vision.

Mr. Pompeo is among the few outsiders to have developed a seemingly close relationship with the president. The two meet each morning for the daily intelligence brief, conducted by the Central Intelligence Agency director. During the meetings, Mr. Pompeo explained the nuances...