A deal for the assets and goodwill of the £400,000-turnover B3 printer was completed on Friday afternoon, with six employees moving across to X1.
The KK name will be saved and it will also remain in its current location, around 40 feet away from X1, for the time being.
Sales director Tim Lance said: "KK's lease runs out later this year but there is no need for the business to be moved at this stage. We can see where we are. At this stage the most important thing is the customers and the employees."
X1 initially approached KK Print Solutions owner Denise Goodacre four years ago, but "the time wasn't right for either party". The businesses began discussing a deal again in December last year. Goodacre will now retire from the business.
Lance added: "We didn't share the same customers as we agreed not to go after each others' customers, so it has opened up a whole new client base. That client base is incredibly loyal to KK and they will still be dealing with all the same people. It is a very strong brand in the area."
X1 now plans to move a number of KK's customers to web-to-print services. In the past three months X1 has seen its web-to-print business increase 80%, while it also jumped 60% in the preceding three months, according to Lance.