Speaking in Brussels on Tuesday, he said, "President-Elect Donald Trump stated during the election campaign that he is a big fan of Nato and I am certain that he will live up to all of the commitments of the United States in the alliance, because a strong Nato is important for Europe but it is also important for the US."
Stoltenberg added, "He also pointed out the importance of increased defence spending - but Europeans are stepping up their efforts to invest more in defence - and I absolutely agree with him that has been a message from US leaders for many years.
"And the good thing is that we now see that Europeans are actually investing more in defence, they are investing more in defence in Europe and they are also contributing to a fairer burden-sharing."
The official was also asked about the relationship between Trump and Russian President Vladimir Putin and whether the time is right to try to normalise relations with Russia.
On this he said, "It's normal for President-Elect Donald Trump speaks to world leaders, including of course the leader of Russia. And the message from Nato has been that we want a dialogue with Russia.
"Russia is our biggest neighbour, Russia is there to stay and especially when tensions run high, especially when we face many different security challenges, it is important to have a chance for an open political dialogue with Russia."
He added, "That is Nato's message and there is no contradiction between strong defence and political dialogue. We think it is important to respect the territorial integrity and sovereignty of all nations, including Ukraine.
"Therefore we will never respect or accept the violation of Ukraine's territorial integrity and sovereignty."
Stoltenberg was at the Council of the EU in Brussels on Tuesday to participate in the meeting of EU ministers of defence and discuss both Nato-EU cooperation and the European defence.
He said, "I welcome the decision made on Monday by the defence ministers and foreign ministers of the EU on the implementation of security and defence of the global strategy.
My message has been, since I became Secretary General of Nato, that Europe has to do more, and invest more in defence and that is what we see is happening, so I welcome that after many years of cuts in defence spending Europe is now increasing defence spending as a response to a more dangerous and more challenging security environment."