United's main business on deadline day was tying Martial down to a new contract.
Solskjaer has won eight of his nine matches in charge of United and there have been calls for the Norwegian to be appointed the club's permanent boss having overseen a huge change since replacing Jose Mourinho in December.
Solskjaer scored 126 goals for Man Utd during 11 seasons in the north-west.
"He knows that I'd like him to do a couple more runs in behind, but I've not seen many players with the quick feet and the skills in the last third as he has so we're going to build his career and hopefully he'll grab the chance with both hands". But after an impressive start to the new campaign which has seen him score 10 goals in 25 games and force his way back into Didier Deschamps' plans he has ended speculation about his future by signing a new deal.
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He also played for the Atlanta Falcons (1992), New Orleans Saints (1993-94), Cowboys (1995-97) and Oakland Raiders (1998). The following season he made the Pro Bowl after throwing a career-high 2,746 yards and 15 touchdowns.
Martial may be slightly ahead of Ronaldo after 104 games but we all know what Ronaldo went on to become at United and beyond, so the Frenchman will need to improve consistently as the season's roll on.
Previously linked with moves to PSG and Juventus, Martial went from being nearly out of the club in pre-season, to become one of the club's top scorers and more productive players.
Speaking to the club's website about the deal, Solskjaer was effusive in his praise for the forward.
Neville believes retaining Martial was the best decision for United, but feels they should now be demanding a considerable return on their sizeable show of faith.
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"When he gets chances he's a fantastic finisher, so he needs to get more chances", said Solskjaer. Anthony has done some rehab work, so he'll try a session today.
"It's a confirmation that we are happy with him and we believe in him he's got fantastic potential", the scorer of the 1999 Champions final victor explained.
"You can talk about Cristiano's career, what he's made, how he's got there and all the fantastic players we've got, so I sat down with Anthony and he wants to be a part of this and we believe the club have got a top player there".
They now find themselves sixth in the Premier League table as they look to try and climb the table under Solskjaer. "This is the ideal club for Anthony to progress his development as a top-class forward and we are all delighted he has signed a long-term deal".
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