Senator Lindsey Graham, R, said in a statement that Pompeo will be more effective on the world stage because foreign leaders will know he speaks for Trump.
Graham also pointed out that as CIA director, Pompeo has been busily circling the globe and establishing relationships that he will now be able to call on as America's top diplomat.
"No one has a stronger relationship with President Trump than Mike Pompeo," Graham said. "This relationship will empower him throughout his tenure as Secretary of State."
Tillerson did have a good personal relationship with Trump, as Trump said on the White House lawn. But Trump always saw Tillerson as pushing back against his instincts and trying to constrain his more controversial initiatives.
"Tillerson was never part of Trump's core strategy team. Pompeo is," said Patrick Cronin, senior fellow at the Centre for a New American Security. "Trump can now have the cohesion in his national security team that he wants."
A White House official told me that Pompeo was simply much better at interacting with Trump, answering even basic questions in a respectful way and incorporating Trump's views into any policy proposal.
"Pompeo showed that you can talk to Trump without seeming to be condescending, something Tillerson struggled with," the official said.
As I reported in November, Pompeo has been quietly preparing to take over the State Department for months.
Since last autumn, co-ordinating with Chief of Staff John Kelly, Pompeo has met and spoken with dozens of foreign policy professionals around Washington to help him prepare for his new job. Those who have spoken with him say he is planning to quickly address the severe staffing vacancies at the top of the State Department and already has many names in mind.
Pompeo will immediately get to choose, in coordination with the White House, new undersecretaries of state and assistant secretaries of state for political affairs, arms sales, intelligence, the Middle East, South Asia, Africa, refugees, human rights, civilian security and much more. Expect traditional Republican hawks who did not sign letters opposing Trump during the GOP primaries.
In a surprise move, the White House has already fired undersecretary for public diplomacy Steve Goldstein. Goldstein issued a statement saying Tillerson had wanted to stay and told reporters Tillerson found out about his firing from Trump's tweet.
"The Secretary did not speak to the President this morning and is unaware of the reason," the statement said. "We wish Secretary-Designate Pompeo well."
Tillerson's chief of staff, Margaret Peterlin, looks likely to depart, as does policy planning director Brian Hook.
On the organisational side, Pompeo is leaning toward discarding much of the State Department reorganisation project Tillerson made his No. 1 mission. The effort has been hugely unpopular inside the building and poorly managed by the leadership team.
Like he did at CIA, Pompeo is expected to shift around portfolios and responsibilities inside the current bureaucratic structure to create less havoc while still emphasising his own priorities.
"As he tries to staff up, he is going to run into two problems," said a former senior national security official in the George W. Bush Administration. "Can he find competent people who are willing to join the Trump administration, and can he get beyond the blacklist?"
Large parts of the State Department professional staff, including the Foreign Service, have experience working for both Republican and Democratic administrations. But they felt neglected and ignored by Tillerson's senior staff, causing a wave of resignations and retirements. If Pompeo can prove early on he respects their contributions, he can stem the bleeding and boost morale.
That would put the State Department back in a position of prominence as the Trump Administration heads into several major diplomatic confrontations. Trump is expected to meet with Kim Jong Un in May, and the State Department has an excellent team of Korea experts who have good relationships with North Korean officials.
The State Department is also working with European countries to negotiate adjustments to the Iran deal, without which Trump has promised to scuttle the agreement in May. As Trump mentioned, Pompeo is much more sceptical of the Iran deal than Tillerson is.
Not everyone is convinced Pompeo will be better for the State Department or US diplomacy than Tillerson.
"Rex Tillerson's tenure as Secretary of State was obviously unsuccessful." said Representative Nita Lowey, the ranking Democrat on the House Appropriations subcommittee on the State Department and foreign operations.
"He was undermined at every turn by the White House, failed to achieve results for the United States on the world stage, and his misguided so-called reorganisation of the State Department has plunged our diplomatic and development corps into crisis. Unfortunately, I see no reason for optimism that Mike Pompeo would be better."
Within the State Department, opinion is decidedly split. People are happy to see Tillerson go but divided on whether Pompeo will be better for them.
"Some people here say the State Department will be more plugged in and he will be a better manager. Other people say he definitely has strong ideological views and are terrified of him," one senior Foreign Service officer told me. "We'll see."
