Koffi, 20, left Ivorian giants ASEC Mimosas and penned a long-term contract with the three-time French champions on Wednesday.
Enyeama, who joined Lille in June 2011 and has made 164 appearances, said he was delighted with the arrival of another African goalkeeper.
"Koffi is a fantastic young goalkeeper and I'm very proud to see another African come to the club," Enyeama told BBC Sport on Thursday.
"It's heart-warming to see a young African goalkeeper earn a move to Europe; it says a lot about his qualities.
"My advice to him is that he should focus on what has brought him to France, keep working hard and concentrate on his job.
"I'll be available to help him settle and give him all the necessary support he needs."
Koffi arrives in Lille with a solid reputation as one of the continent's finest goalkeepers when it comes to one-on-one situations.
Other African players who have used Lille as a springboard to bigger things include Ivory Coast forward Gervinho, Nigerian Peter Odemwingie, Senegal striker Moussa Sow and Cameroon's Jean Makoun.
Koffi joined ASEC Mimosas from Racing club de Bobo-Dioulasso in his native Burkina Faso in December 2015 and helped the club to the 2017 Ivorian title.
Then his country third-choice goalkeeper, Koffi made his international debut as a late substitute against Uganda in March 2016.
He eventually took over the number one jersey from veteran Daouda Diakité in October last year.
Koffi has kept goal for the Stallions in their last nine internationals and played all six matches as the Burkinabe finished third at this year's Africa Cup of Nations in Gabon.
Lille have also snapped up Ivory Coast international Nicolas Pepe from French rivals Angers.
Tthe 22-year-old has signed a five-year deal.
Former Nigeria goalkeeper Vincent Enyeama has welcomed the signing of Burkina Faso international Herve Koffi by the French Ligue 1 side, Lille.