In other news, Kagawa extends stay at Dortmund and LA Galaxy coy on Ibrahimovic talk.
Transfer news: Real Madrid sign Ceballos after Barcelona agree deal with Semedo
Real Madrid have signed Spain Under 21 midfielder Dani Ceballos from Real Betis.
Ceballos, 20, has put pen to paper on a six-year contract with Madrid and will be presented at the Bernabeu next Thursday, the European and Spanish champions announced in a statement on their website.
Ceballos, who was named player of the tournament at the European U21 Championship last month as Spain finished runners-up, will then link up with his new teammates on their pre-season tour of the United States.
Neither club have announced a fee for the Andalusian but reports in Spain suggest Madrid will pay in the region of €17 million (Dh71.2m) for a player who has made 65 Primera Liga appearances for Betis since his debut at the age of 17 in 2014.
Ceballos joins Theo Hernandez, Jesus Vallejo, Marcos Llorente and Borja Mayoral as new additions to Zinedine Zidane's Madrid squad this summer.
Barcelona to sign Semedo
Earlier, Barcelona agreed a deal to sign Portugal defender Nelson Semedo from Benfica.
The 23-year-old right-back will undergo a medical with Barcelona on Friday ahead of what Spanish media are reporting will be a €30 million (Dh125.6m) transfer.
A Barcelona statement said: "Pending medical tests on Friday, the Portuguese international right-back will reinforce Barca's defence.
"Nelson Semedo is one of the brightest youngsters at Benfica. The right-back has progressed quickly to the highest level, both with his club and the Portuguese national side, whom he represented at the last Confederations Cup."
Deulofeu returns to Barca
Meanwhile, Gerard Deulofeu has officially completed his move back to Barcelona from Everton.
The 23-year-old forward passed a medical on Friday morning before signing a two-year contract tying him to the Spanish giants until June 30, 2019.
Barca last month activated the buy-back clause in Deulofeu's contract with Everton to bring him back to the Nou Camp, where he came up through the youth ranks before moving to England in a permanent deal in 2015.
Kagawa signs new deal with Borussia Dortmund
Borussia Dortmund midfielder Shinji Kagawa has signed a contract extension to keep him at the Bundesliga club until June 2020.
The 28-year-old Japan international, who re-joined Dortmund from Manchester United in 2014, helped the club win the German league title in 2011 and 2012 during his first spell at the Westfalenstadion.
"We are really happy that Shinji will continue to play for us in the coming three years," Dortmund sporting director Michael Zorc told the club's official website. "Shinji closely identifies with our club, with the city, and with our fans."
Kagawa has scored 27 goals in 88 appearances for Japan.
Honda leaves Milan for Mexico
Japan attacking midfielder Keisuke Honda has joined Mexican side Pachuca, the Concacaf Champions League holders announced on Friday, two months after leaving AC Milan as a free agent.
"I have just signed for Pachuca and I'm very happy," Honda said in Spanish in a video on the club's Twitter feed.
The club did not disclose the details of his contract.
Honda, 31, has 86 caps for Japan, scoring 36 goals, and is the only Japanese player to score in two separate World Cups, netting in the 2010 and 2014 tournaments.
LA Galaxy coy over Ibrahimovic talk
The Los Angeles Galaxy are on the lookout for a "world-class" signing, but manager Curt Onalfo would not confirm whether Zlatan Ibrahimovic was in their crosshairs.
David Beckham, Steven Gerrard and Robbie Keane are among the stars to have played for Major League Soccer's most successful side over recent years.
Ibrahimovic has long been linked with a move to the StubHub Center, with a £6 million(Dh28.5m)-a-year deal reported to be on the table for the injured striker following his exit from Manchester United.
Galaxy manager Onalfo was coy on such talk - "our policy is not to comment on players that are not part of our team" - but was more forthcoming about their grand plans.
Asked if they had room for a marquee player, he said: "Absolutely. We always have. The DNA of the Galaxy is to attract world-class players, so we're always looking for one."
Ibrahimovic, 35, is set to be out until the new year after sustaining serious knee ligament damage playing for United in April.