Your original could be a command telling some unknown persons to welcome the students and teachers, or an incomplete version of the sentence "We would like to welcome back our students as well as our teachers."
In your banner, you don't want a full sentence, just a greeting/salutation of "Welcome back." like "Hello, John."
Welcome back, students and teachers.
"Welcome back to our students and teachers." could be read as "We would like to say "Welcome back" to our students and teachers." but it's rather long for a banner.