Inclusion Criteria  Be a Japanese person. Participant must have a documented diagnosis of a form of primary humoral immunodeficiency involving antibody formation and requiring gammaglobulin replacement, as defined according to the International Union of Immunological Societies(IUIS) Committee 2017. The diagnosis must be confirmed by the Medical Director prior to TAK-771 treatment. Participant has been receiving a stable clinical dose of intravenous immunoglobulin (IVIG) or conventional subcutaneous immunoglobulin (cSCIG), which is equivalent to approximately 200 to 600 mg/kg body weight per 3 to 4 week period for IVIG and approximately 50 to 200 mg/kg body weight per week for cSCIG based on the description in the package insert, consistently over a period of at least 3 months prior to screening, or Participant has been receiving of TAK-664 with fixed dose and dosing frequency at least 3 months prior to enrollment. That is, participant is about to complete Study TAK-664-3001 or participating in Study TAK-664-3002. Participant who has been receiving IVIG or cSCIG had all serum trough levels of total immunoglobulin G (IgG) >=5 g/L within 1 month prior to the screening/enrollment.  Serum trough levels at screening/enrollment meet one of the following:  IVIG-treated or cSCIG-treated participants Participant who had serum trough levels of IgG >=5 g/L at the last 2 points in screening procedure before the first administration of TAK-771. TAK-664-treated participants Participant who had serum trough levels of IgG >=5 g/L at the last 2 points in TAK-664 studies before the first administration of TAK-771. Participant is willing and able to comply with use of digital tools and applications.  Exclusion Criteria  Participant has a known history of or is positive at screening/enrollment for one or more of the following: hepatitis B surface antigen (HbsAg), polymerase chain reaction (PCR) for hepatitis C virus (HCV), PCR for human immunodeficiency virus (HIV) Type 1/2 For participants who are switching from TAK-664 studies, the eligibility will be reconfirmed after result of the specialty test conducted at Week 1 become available.  Abnormal laboratory values at screening/enrollment meeting any one of the following criteria (abnormal tests may be repeated once to determine if they are persistent):  Persistent alanine aminotransferase (ALT) and aspartate aminotransferase (AST) >2.5 times the upper limit of normal (ULN) for the testing laboratory Persistent severe neutropenia (defined as an absolute neutrophil count [ANC] =<500/mm^3) Participant has presence of renal function impairment defined by eGFR <60 mL/min/1.73m^2. Participant has been diagnosed with, or had a malignancy (other than adequately treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix) unless the disease-free period prior to screening exceeds 5 years. Participant is receiving anti-coagulation therapy or has a history of thrombotic episodes (including deep vein thrombosis, myocardial infarction, cerebrovascular accident, pulmonary embolism) within 12 months prior to screening/enrollment or a history of thrombophilia. Participant has abnormal protein loss (protein losing enteropathy, nephrotic syndrome) Participant has anemia that would preclude phlebotomy for laboratory studies according to standard practice at the site. Participant has an ongoing history of hypersensitivity or persistent reactions (urticaria, breathing difficulty, severe hypotension, or anaphylaxis) following IVIG, subcutaneous immunoglobulin (SCIG), and/or Immune Serum Globulin infusions Participant has immunoglobulin A (IgA) deficiency (IgA less than 0.07g/L), known anti-IgA antibodies, and a history of hypersensitivity. Participant is on preventative (prophylactic) systemic antibacterial antibiotics at doses sufficient to treat or prevent bacterial infections, and cannot stop these antibiotics at the time of screening/enrollment. Participant has active infection and is receiving antibiotic therapy for the treatment of infection at the time of screening/enrollment or had a serious bacterial infection within the 3 months prior to screening/enrollment Participant has a bleeding disorder, or a platelet count less than 20,000/microL, or in the opinion of the investigator, would be at significant risk of increased bleeding or bruising as a result of subcutaneous (SC) therapy. Participant has total protein >9 g/dL or myeloma, or macroglobulinemia (IgM) or paraproteinemia. Participant has a known allergy to hyaluronidase Participant has severe dermatitis that would preclude adequate sites for safe product administration.