The coach, who has seen the club rise from relegation candidates to Champions League position contenders within 12 months, is wanted by the England national team.
Howe is the favorite for bookies to succeed Gareth Southgate after this winter's FIFA World Cup in Qatar.
“I'm absolutely proud on honoured to be here managing this unbelievable football club," Howe told reporters following the 1-0 win over Chelsea.
“My only focus is on Newcastle.
“Now, my focus is probably to have a couple of days with my family, and then reset on our training and all the processes that I need to make sure that we hit the ground running in the second half of the season."