However, after Sunday's 4-2 win at Celta, the club are sixth, four points behind leaders Barca.
Solari took charge of the first team a fortnight ago and promptly racked up the best start of any new manager at the club in its 116 year history.
Solari was handed the reins on a temporary two-week basis on Oct 29 after Lopetegui had overseen a miserable run that included just one victory in seven games. "Real Madrid have worked out his contract and there are no problems", the Spanish football federation stated.
The last of those, a 5-1 thumping at the hands of Barcelona, proved the final straw for club president Florentino Perez but the team have rebounded under their new coach.
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This is Solari's maiden job in charge of a first team. It's a great opportunity.
Happy with the national team coach: "Right from the start, Luis Enrique has given me a lot of confidence; he looks out for me and gives me a lot of advice and that's important for a player".
The challenge for Solari will be to manage the dressing room when results take a turn for the worse.
In his final game as interim coach over the weekend before the worldwide break, Solari saw Real win 4-2 against Celta Vigo.
Solari made his professional debut as a player with River Plate in 1996 before leaving his native Argentina in in 1999 to play for Atletico Madrid and then Real Madrid, where he won seven titles in five seasons between 2000-05.