This study will evaluate if testosterone solution can raise testosterone hormone levels into the normal range after treatment for up to 9 Weeks, in those participants with a documented history of subtherapeutic levels [total testosterone <300 nanograms per deciliter (ng/dL)] when previously treated with a topical testosterone gel.

Inclusion Criteria:

• Able to read, understand, and provide signed informed consent before starting trial activities related to this study (including discontinuing testosterone replacement therapy prior to Screening)
• Male participants with a diagnosis of hypogonadism and documented biochemical failure (total testosterone <300 ng/dL) when treated with the highest dose of a topical testosterone gel tolerated by the participant. Documentation of biochemical failure includes: the name and dose of the topical testosterone gel, a lab report showing a total testosterone level <300 ng/dL while on therapy, or a written chart report stating that there was a clear lack of efficacy, including the participant's serum total testosterone level at the time of failure
• Screening serum total testosterone level of <300 ng/dL (based on the average of 2 morning blood samples taken at least 30 minutes apart) at Screening
• Prostate Specific Antigen (PSA) <4 nanogram per milliliter (ng/mL) at Screening
• If the participant is receiving testosterone replacement therapy and is willing to discontinue testosterone replacement therapy to enter the study, their screening total testosterone level cannot be checked until at least 14 days after discontinuing topical therapies, or after at least 28 days for participants using short-acting intramuscular (IM) therapies

Exclusion Criteria:

• Any previous treatment with testosterone topical solution (LY900011)
• Known or suspected carcinoma (or history of carcinoma) of the prostate or suspicious nodules on digital rectal exam at Screening
• Known or suspected breast cancer or history of breast cancer
• Severe sleep apnea (untreated or unsuccessfully treated) in the opinion of the study investigator
• Use of long-acting IM testosterone undecanoate in the 6-month period prior to Screening
• History of the use of an implanted testosterone pellets (Testopel)
• International Prostate Symptom Score (IPSS) total score >19 at Screening
• Hematocrit ≥50% at Screening. For sites located at elevations ≥4500 feet, participants will be excluded with hematocrit >54% according to investigator discretion. Any participant with a hematocrit >54% at later study visits will be withdrawn from the study
• Significant history of allergy and/or sensitivity to the drug products or excipients, including any history of sensitivity to testosterone and/or sunscreens
• Dermatologic condition in underarm area that might interfere with testosterone absorption (for example, eczema) or that could be exacerbated by topical testosterone replacement therapy
• History of luteinizing hormone-releasing hormone (LHRH) antagonist or agonist treatment in the 6 months prior to Screening
• Exhibit any evidence of congestive heart failure [New York Heart Association (NYHA) Class 2 or above] within 6 months prior to Screening
• Exhibit evidence of severe renal impairment [creatinine clearance <30 milliliter per minute (mL/min) as determined by the Cockcroft-Gault formula] at Screening
• Exhibit a history of severe liver disease or clinical evidence of hepatic impairment at Screening
• Any condition that would interfere with the participant's ability to provide informed consent, or comply with study instructions, or would place the participant at increased risk, or might confound the interpretation of the study results
• Are investigator site personnel directly affiliated with this study and/or their immediate families. Immediate family is defined as a spouse, parent, child, or sibling, whether biological or legally adopted
• Are currently enrolled in, or discontinued within the last 30 days from, a clinical trial involving an investigational product or non-approved use of a drug or device (other than the investigational product used in this study), or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study