Strasbourg have paid for 70% of Ortega's rights, with Real Madrid retaining the remaining share and the 20-year-old set to travel to France in the coming hours to undergo a medical and sign his contract, according to the club's own reporting.
Ortega began last season with Real Madrid C, where he was a key figure in the club's Youth League triumph, scoring the equaliser in the final against Club Brugge to send the match to penalties, before also featuring for Castilla in the closing stages of the campaign.
He finished the season with 18 goals in 55 appearances across the three levels — eight for Real Madrid C, six for Castilla and four for the Juvenil A side — form that persuaded Strasbourg to make an unusually large investment in a player yet to appear for any club's first team.
Ortega has spent his entire youth career at Real Madrid's academy, working his way up through the club's junior sides before breaking into the Youth League squad. His finishing and movement in behind defences had already made him one of the most closely followed prospects at Valdebebas, and interest from clubs across Europe had been building throughout the second half of last season as his Youth League form drew wider attention.
The sale continues a lucrative summer for Real Madrid's academy, which has generated significant income even as head coach José Mourinho oversees a squad shaped by high-profile signings elsewhere.
Jacobo's departure follows those of Nico Paz, Gonzalo García, Víctor Muñoz, Gila, Álvaro Rodríguez, Álex Jiménez, César Palacios, Victor Valdepeñas, Fran García, Mario Martín and Fran González, with Nico Paz's permanent exit to Como alone bringing in €66m and Gonzalo García's move to Fulham worth €40m for 66% of his rights.
César Palacios also joined Fulham this summer, in a separate €10m deal, reuniting with former Real Madrid player Álvaro Arbeloa, who now manages the London club.
For Strasbourg, eighth in Ligue 1 last season, the deal represents a significant bet on a player considered one of the most exciting attacking prospects to come through Real Madrid's academy system in recent years.
The French club have built a reputation in recent seasons for recruiting promising young talent from across Europe's top academies, and Ortega's arrival fits that pattern as they look to build on last season's mid-table finish.