Mr Gates will hold talks with Afghan President Hamid Karzai and meet US troops serving in the country.
Speaking to reporters in Kabul, he said he would tell soldiers the US was "in this thing to win".
Mr Gates is the most senior US official to visit Afghanistan after President Barack Obama announced he was deploying 30,000 extra US troops to the country.
Speaking to reporters on the flight to Kabul, Mr Gates said he would tell Afghan officials the US intends "to be their partner for a long time".
He said he would discuss with Mr Karzai the US decision to send further troops and how it would be implemented.
But he said they would also talk about how to better train up Afghan security forces for an eventual US withdrawal.
"As the security situation improves and we're able, over time, to reduce our forces, the civilian, developmental, economic and other kinds of relations between us will become the predominant part of the relationship," the Reuters news agency quoted him as saying.
Mr Obama has ordered 30,000 more US troops to be sent to Afghanistan as quickly as possible, bringing US troop strength in the country to more than 100,000.
Nato allies in Afghanistan have agreed to contribute another 7,000 soldiers between them.
Announcing the surge, Mr Obama said the mission in Afghanistan was to defeat al-Qaeda, reverse the Taliban's momentum and deny them the ability to overthrow the government.
Corruption
The president has said the US will start to pull out of Afghanistan by July 2011.
But the BBC's Martin Patience in Kabul says Mr Gates will want to reassure Mr Karzai that the withdrawal will depend on the situation on the ground and the adequate training of Afghan security forces.
Mr Gates is also expected to use his visit to discuss efforts to curb corruption in Afghanistan.
Mr Karzai, who was recently re-elected in a poll marred by widespread fraud, is expected to name his new cabinet within days.
Mr Gates said the US would be "watching the appointments that get made" and that it was important to have "capable and honest ministers" in the crucial roles, the Associated Press news agency reported.
The US is running out of patience with Afghan promises to tackle corruption and now wants to see clear action taken against senior officials found to be corrupt, says our correspondent.
On Monday, the mayor of Kabul was sentenced in his absence to four years in prison for corruption, on charges related to more than $16,000 (£9,800) of public money.
Abdul Ahad Sahebi's, whose whereabouts are not known, was the first high profile official to face such charges under Mr Karzai's second term.
