Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The Romanian has been at the club since 2004, winning the league six times as well as the UEFA Cup in 2009.
Lucescu's contract was due to expire at the end of the season and the 67-year-old had been linked with a return to management in Italy, where he was previously in charge of Inter Milan.
However Shakhtar have tied him down to a new deal, much to the delight of club president, Rinat Akhmetov.
"When we talked about a contract, the issue of money was not an issue because it's not important for me nor for Mr Lucescu," he told the official Shakhtar website.
"I was interested in only one major thing: whether this team has reached the maximum, or it can take a step forward? Mister told me simply: "I love our fans. I love our players. I believe in my assistants".
"I am confident that together with the club, joining efforts, we are able to conquer new heights."
The club are currently 15 points clear of rivals Metalist at the top of the Ukrainian Premier League table.