United States international Johnson agreed a deal to move from Hoffenheim in February, while Sommer's switch from Basel was confirmed a month later.
Both were unveiled at Monchengladbach on Wednesday and Johnson - a versatile defender with plenty of Bundesliga experience - is eager to get going at Borussia Park.
"I was looking for a new challenge and Borussia has very early on to get me," said the former Hoffenheim and Wolfsburg man.
"Borussia are playing in the Europa League, which excites me, and that tempted me.
"No player should be satisfied with what he has achieved so far, but should always want more. It is the same with me too. I want to develop myself and help the team to have success."
Switzerland international Sommer joins as a replacement for goalkeeper Marc-Andre ter Stegen, who has gone to Barcelona.
However, Sommer is not thinking about the legacy of the highly-rated 22-year-old - instead preferring to focus on his own performances.
"I know how big the boots I'm stepping into are. Marc had a great time and some super years with Borussia," explained Sommer, who was part of the Swiss squad at the World Cup in Brazil.
"He's a complete goalkeeper and is taking the next step at Barcelona. I don't want to forget about him.
"I'd just like to be a good goalkeeper and I don't feel pressure about being his successor."
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