Bayern Munich have signed France defender Dayot Upamecano from July 1 after meeting his £38m release clause, while Angelino has joined RB Leipzig for £16m from Manchester City after almost two years on loan.
The RB Leipzig centre-back, 22, had been heavily linked with a number of Premier League clubs including Manchester United and Liverpool.
But, instead, he has chosen to sign a five-year contract with the European champions.
“We’re convinced that Dayot will be a very important member of our team in the coming years,” said Bayern board member Hasan Salihamidzic.
Upamecano, who has three caps for France, joined Leipzig from RB Salzburg in 2017 and has become one of the most highly-rated defenders in Europe.
RB Leipzig chief executive Oliver Mintzlaff says Upamecano, who will line up for the German side in the Champions League against Liverpool this week, indicated he wanted to move on.
“Of course, we would have liked to keep Dayot Upamecano at RB Leipzig. However, Dayot indicated to us very fairly and in good time that he would like a new challenge this summer and take the next step,” Mintzlaff said.
“Dayot has shown outstanding development during his time in Leipzig, which is exemplary for our philosophy of finding young talents and consistently bringing them to the top level.
“Dayot has been and remains an important factor in our success and FC Bayern can look forward to an outstanding footballer and great person.”
Spanish full-back Angelino has signed a deal with Leipzig until 2025 after spending the past two seasons with the club.
The 24-year-old has scored nine goals and provided 16 assists in an impressive spell in Germany.
Leipzig had the option to convert the loan into a permanent deal, and have duly done so.
"Angelino is an extremely good player who is very important for our game," said head coach Julian Nagelsmann.
"From the start, he played a key role for us and although he's already developed very well and very quickly, he still has a lot more potential."